Combining TT* argument and bilinear interpolation,this paper obtains the Strichartz and smoothing estimates of dispersive semigroup e^(-itP(D)) in weighted L^(2) spaces.Among other things,we recover the results in[1]....Combining TT* argument and bilinear interpolation,this paper obtains the Strichartz and smoothing estimates of dispersive semigroup e^(-itP(D)) in weighted L^(2) spaces.Among other things,we recover the results in[1].Moreover,the application of these results to the well-posedness of some equations are shown in the last section.展开更多
Earthquakes can cause significant damage and loss of life,necessitating immediate assessment of the resulting fatalities.Rapid assessment and timely revision of fatality estimates are crucial for effective emergency d...Earthquakes can cause significant damage and loss of life,necessitating immediate assessment of the resulting fatalities.Rapid assessment and timely revision of fatality estimates are crucial for effective emergency decisionmaking.This study using the February 6,2023,M_(S)8.0 and M_(S)7.9 Kahramanmaras,Türkiye earthquakes as an example to estimate the ultimate number of fatalities.An early Quick Rough Estimate(QRE)based on the number of deaths reported by the Disaster and Emergency Management Presidency of Türkiye(AFAD)is conducted,and it dynamically adjusts these estimates as new data becomes available.The range of estimates of the final number of deaths can be calculated as 31384–56475 based on the"the QRE of the second day multiplied by 2–3" rule,which incorporates the reported final deaths 50500.The Quasi-Linear and Adaptive Estimation(QLAE)method adaptively adjusts the final fatality estimate within two days and predicts subsequent reported deaths.The correct order of magnitude of the final death toll can be estimated as early as 13 hr after the M_(S)8.0 earthquake.In addition,additional earthquakes such as May 12,2008,M_(S)8.1 Wenchuan earthquake(China),September 8,2023,M_(S)7.2 Al Haouz earthquake(Morocco),November 3,2023,M_(S)5.8 Mid-Western Nepal earthquake,December 18,2023,M_(S)6.1 Jishishan earthquake(China),January 1,2024,M_(S)7.2 Noto Peninsula earthquake(Japan)and August 8,2023,Maui,Hawaii,fires are added again to verified the correctness of the model.The fatalities from the Maui fires are found to be approximately equivalent to those resulting from an M_(S)7.4 earthquake.These methods complement existing frameworks such as Quake Loss Assessment for Response and Mitigation(QLARM)and Prompt Assessment of Global.展开更多
In this paper, we derive the a priori estimates for a class of more general (k, l)-Hessian quotient type equations involving u and Du on the right hand function. As an application we prove the Liouville theorem depend...In this paper, we derive the a priori estimates for a class of more general (k, l)-Hessian quotient type equations involving u and Du on the right hand function. As an application we prove the Liouville theorem depending on Pogorelov type estimates. On the other hand, we obtain the existence and uniqueness of the k-admissible solution for these general equations with the Neumann boundary condition, based on some growth conditions for the right hand function.展开更多
This paper is devoted to the Polynomial Preserving Recovery (PPR) based a posteriori error analysis for the second-order elliptic non-symmetric eigenvalue problem. An asymptotically exact a posteriori error estimator ...This paper is devoted to the Polynomial Preserving Recovery (PPR) based a posteriori error analysis for the second-order elliptic non-symmetric eigenvalue problem. An asymptotically exact a posteriori error estimator is proposed for solving the convection-dominated non-symmetric eigenvalue problem with non-smooth eigenfunctions or multiple eigenvalues. Numerical examples confirm our theoretical analysis.展开更多
In this article,we are concerned with the C^(2)estimates for the k-convex solutions of a class of degenerate k-Hessian equations on closed Hermitian manifolds,whose function in the right-hand side is relevant to the u...In this article,we are concerned with the C^(2)estimates for the k-convex solutions of a class of degenerate k-Hessian equations on closed Hermitian manifolds,whose function in the right-hand side is relevant to the unknown function and its gradient.We will get C^(0)estimate by promoting others′results,and get the“HMW estimate”of this equation such that the conditions of using blow-up analysis are satisfied,and the gradient estimate and second-order estimate will be obtained.Such an estimate will be helpful to study the existence for the solution of the equation.展开更多
In this paper,we study and characterize the volume estimates of geodesic balls on Finsler gradient Ricci solitons.We get the upper bounds on the volumes of geodesic balls of all three kinds of Finsler gradient Ricci s...In this paper,we study and characterize the volume estimates of geodesic balls on Finsler gradient Ricci solitons.We get the upper bounds on the volumes of geodesic balls of all three kinds of Finsler gradient Ricci solitons under certain condition about the Laplacian of thedistance function.展开更多
Cropland nitrate leaching is the major nitrogen(N) loss pathway, and it contributes significantly to water pollution. However, cropland nitrate leaching estimates show great uncertainty due to variations in input data...Cropland nitrate leaching is the major nitrogen(N) loss pathway, and it contributes significantly to water pollution. However, cropland nitrate leaching estimates show great uncertainty due to variations in input datasets and estimation methods. Here, we presented a re-evaluation of Chinese cropland nitrate leaching, and identified and quantified the sources of uncertainty by integrating three cropland area datasets, three N input datasets, and three estimation methods. The results revealed that nitrate leaching from Chinese cropland averaged 6.7±0.6 Tg N yr^(-1)in 2010, ranging from 2.9 to 15.8 Tg N yr^(-1)across 27 different estimates. The primary contributor to the uncertainty was the estimation method, accounting for 45.1%, followed by the interaction of N input dataset and estimation method at 24.4%. The results of this study emphasize the need for adopting a robust estimation method and improving the compatibility between the estimation method and N input dataset to effectively reduce uncertainty. This analysis provides valuable insights for accurately estimating cropland nitrate leaching and contributes to ongoing efforts that address water pollution concerns.展开更多
We consider the space and time decays of certain problems within the second gradient thermal law.Notably,for this thermal theory,the exponential time decay is precluded.First,the time estimates of polynomial type are ...We consider the space and time decays of certain problems within the second gradient thermal law.Notably,for this thermal theory,the exponential time decay is precluded.First,the time estimates of polynomial type are obtained for both the thermal equation and the one-dimensional thermoelastic system,where the impossibility of localization with respect to time is also established.Then,the space estimates are deduced for the multidimensional thermoelastic problem,which allow to show the exponential decay of the energy.展开更多
The paper is concerned with a class of elliptic equation with critical exponent and Dipole potential.More precisely,we make use of the refined Sobolev inequality with Morrey norm to obtain the existence and decay prop...The paper is concerned with a class of elliptic equation with critical exponent and Dipole potential.More precisely,we make use of the refined Sobolev inequality with Morrey norm to obtain the existence and decay properties of nonnegative radial ground state solutions.展开更多
In this paper,we give improved error estimates for linearized and nonlinear CrankNicolson type finite difference schemes of Ginzburg-Landau equation in two dimensions.For linearized Crank-Nicolson scheme,we use mathem...In this paper,we give improved error estimates for linearized and nonlinear CrankNicolson type finite difference schemes of Ginzburg-Landau equation in two dimensions.For linearized Crank-Nicolson scheme,we use mathematical induction to get unconditional error estimates in discrete L^(2)and H^(1)norm.However,it is not applicable for the nonlinear scheme.Thus,based on a‘cut-off’function and energy analysis method,we get unconditional L^(2)and H^(1)error estimates for the nonlinear scheme,as well as boundedness of numerical solutions.In addition,if the assumption for exact solutions is improved compared to before,unconditional and optimal pointwise error estimates can be obtained by energy analysis method and several Sobolev inequalities.Finally,some numerical examples are given to verify our theoretical analysis.展开更多
In this paper,the higher order asymptotic behaviors of boundary blow-up solutions to the equation■in bounded smooth domain■are systematically investigated for p and q.The second and third order boundary behaviours o...In this paper,the higher order asymptotic behaviors of boundary blow-up solutions to the equation■in bounded smooth domain■are systematically investigated for p and q.The second and third order boundary behaviours of the equation are derived.The results show the role of the mean curvature of the boundary■and its gradient in the high order asymptotic expansions of the solutions.展开更多
An H^1-Galerkin mixed finite element method is discussed for a class of second order SchrSdinger equation. Optimal error estimates of semidiscrete schemes are derived for problems in one space dimension. At the same t...An H^1-Galerkin mixed finite element method is discussed for a class of second order SchrSdinger equation. Optimal error estimates of semidiscrete schemes are derived for problems in one space dimension. At the same time, optimal error estimates are derived for fully discrete schemes. And it is showed that the H1-Galerkin mixed finite element approximations have the same rate of convergence as in the classical mixed finite element methods without requiring the LBB consistency condition.展开更多
A mobile C-band dual polarimetric weather radar J type （PCDJ）, which adopts simultaneous transmission and simultaneous reception （STSR） of horizontally and vertically polarized signals, was first developed in Chin...A mobile C-band dual polarimetric weather radar J type （PCDJ）, which adopts simultaneous transmission and simultaneous reception （STSR） of horizontally and vertically polarized signals, was first developed in China in 2008. It was deployed in the radar observation plan in the South China Heavy Rainfall Experiment （SCHeREX） in the summer of 2008 and 2009, as well as in Tropical Western Pacific Ocean Observation Experiments and Research on the Predictability of High Impact Weather Events from 2008 to 2010 in China （TWPOR）. Using the observation data collected in these experiments, the radar systematic error and its sources were analyzed in depth. Meanwhile an algorithm that can smooth differential propagation phase （~Dp） for estimating the high-resolution specific differential phase （KDP） was developed. After attenuation correction of reflectivity in horizontal polarization （ZH） and differential reflectivity （ZDR） of PCDJ radar by means of KDP, the data quality was improved significantly. Using quality-controlled radar data, quantitative rainfall estimation was performed, and the resutls were compared with rain-gauge measurements. A synthetic ZH /KDp-based method was analyzed. The results the traditional ZH-based method when the rain suggest that the synthetic method has the advantage over rate is 〉5 mm h^-1. The more intensive the rain rates, the higher accuracy of the estimation.展开更多
The Ice,Cloud and Land Elevation Satellite-2(ICESat-2),a new spaceborne light detection and ranging(LiDAR)system,was successfully launched on September 15,2018.The ICESat-2 data increase the types of spaceborne LiDAR ...The Ice,Cloud and Land Elevation Satellite-2(ICESat-2),a new spaceborne light detection and ranging(LiDAR)system,was successfully launched on September 15,2018.The ICESat-2 data increase the types of spaceborne LiDAR data archive and provide new control point data for large-scale topographic mapping and geodetic surveying.However,the accuracy of the ATL 08 terrain estimates has not been fully evaluated on a large scale and in complex terrain conditions.This article aims to quantitatively assess the accuracy of ICESat-2 ATL 08 terrain estimates.Firstly,the ICESat-2 ATL 08 terrain estimates were compared with the high-precision airborne LiDAR digital terrain model(DTM),and impacts of acquisition time,vegetation cover type,terrain slope,and season change on the terrain estimation accuracy were analyzed.We get the following conclusions from the analysis:1)the mean and RMSE of the terrain estimates of day acquisitions are 0.22 m and 0.59 m higher than that of night acquisitions;2)the accuracy of the ATL 08 terrain estimates acquired in vegetated areas is lower than those in non-vegetated areas;3)the accuracy of the ATL 08 terrain estimates is inversely proportional to the slope,and the elevation error increases significantly when the terrain slope is larger than 30°;4)in the non-vegetation covered area,the accuracy of the ATL 08 terrain estimates of summer and winter acquisitions has no obvious discrepancy,but in vegetated area,the accuracy of winter acquisitions is significantly better than that of summer acquisitions.This research provides references for the selection and application of ICESat-2 data.展开更多
Satellite-based products with high spatial and temporal resolution provide useful precipitation information for data-sparse or ungauged large-scale watersheds. In the Lower Lancang-Mekong River Basin, rainfall station...Satellite-based products with high spatial and temporal resolution provide useful precipitation information for data-sparse or ungauged large-scale watersheds. In the Lower Lancang-Mekong River Basin, rainfall stations are sparse and unevenly distributed, and the transboundary characteristic makes the collection of precipitation data more difficult, which has restricted hydrological processes simulation. In this study, daily precipitation data from four datasets(gauge observations, inverse distance weighted(IDW) data, Tropical Rainfall Measuring Mission(TRMM) estimates, and Climate Hazards Group InfraRed Precipitation with Stations(CHIRPS) estimates), were applied to drive the Soil and Water Assessment Tool(SWAT) model, and then their capability for hydrological simulation in the Lower Lancang-Mekong River Basin were examined. TRMM and CHIRPS data showed good performances on precipitation estimation in the Lower Lancang-Mekong River Basin, with the better performance for TRMM product. The Nash-Sutcliffe efficiency(NSE) values of gauge, IDW, TRMM, and CHIRPS simulations during the calibration period were 0.87, 0.86, 0.95, and 0.93 for monthly flow, respectively, and those for daily flow were 0.75, 0.77, 0.86, and 0.84, respectively. TRMM and CHIRPS data were superior to rain gauge and IDW data for driving the hydrological model, and TRMM data produced the best simulation performance. Satellite-based precipitation estimates could be suitable data sources when simulating hydrological processes for large data-poor or ungauged watersheds, especially in international river basins for which precipitation observations are difficult to collect. CHIRPS data provide long precipitation time series from 1981 to near present and thus could be used as an alternative precipitation input for hydrological simulation, especially for the period without TRMM data. For satellite-based precipitation products, the differences in the occurrence frequencies and amounts of precipitation with different intensities would affect simulation results of water balance components, which should be comprehensively considered in water resources estimation and planning.展开更多
In this paper, under the hypothesis that y is upper bounded, we construct a Lyapunov functional for the multidimensional isentropic compressible magnetohydrodynamic equations and show that the weak solutions decay exp...In this paper, under the hypothesis that y is upper bounded, we construct a Lyapunov functional for the multidimensional isentropic compressible magnetohydrodynamic equations and show that the weak solutions decay exponentially to the equilibrium state in L2 norm. Our result verifies that the method of Daoyuan Fang, Ruizhao Zi and Ting Zhang I1] can be adapted to magnetohydrodynamic equations.展开更多
Let （M,g, e^-fdv） be a smooth metric measure space. In this paper, we con- sider two nonlinear weighted p-heat equations. Firstly, we derive a Li-Yau type gradient estimates for the positive solutions to the followi...Let （M,g, e^-fdv） be a smooth metric measure space. In this paper, we con- sider two nonlinear weighted p-heat equations. Firstly, we derive a Li-Yau type gradient estimates for the positive solutions to the following nonlinear weighted p-heat equationand f is a smooth function on M under the assumptionthat the m-dimensional nonnegative Bakry-Emery Ricci curvature. Secondly, we show an entropy monotonicity formula with nonnegative m-dimensional Bakry-Emery Ricci curva- ture which is a generalization to the results of Kotschwar and Ni [9], Li [7].展开更多
A nonlinear parabolic system is derived to describe incompressible nuclear waste-disposal contamination in porous media. A sequential implicit tirne-stepping is defined, in which the pressure and Darcy velocity of the...A nonlinear parabolic system is derived to describe incompressible nuclear waste-disposal contamination in porous media. A sequential implicit tirne-stepping is defined, in which the pressure and Darcy velocity of the mixture are approximated simultaneously by a mixed finite element method and the brine, radionuclid and heat are treated by a combination of a Galerkin finite element method and the method of characteristics. Optimal-order convergence in L2 is proved. Time-truncation errors of standard procedures are reduced by time stepping along the characteristics of the hyperbolic part of the brine, radionuclide and heal equalios, temporal and spatial error are lossened by direct compulation of the velocity in the mixed method, as opposed to differentiation of the pressure.展开更多
The trend estimate of vegetation change is essential to understand the change rule of the ecosystem.Previous studies were mainly focused on quantifying trends or analyzing their spatial distribution characteristics.Ne...The trend estimate of vegetation change is essential to understand the change rule of the ecosystem.Previous studies were mainly focused on quantifying trends or analyzing their spatial distribution characteristics.Nevertheless,the uncertainties of trend estimates caused by spatiotemporal scale effects have rarely been studied.In response to this challenge,this study aims to investigate spatiotemporal scale effects on trend estimates using Moderate-Resolution Imaging Spectroradiometer(MODIS)Normalized Difference Vegetation Index(NDVI)and Gross Primary Productivity(GPP)products from 2001 to 2019 in the Qinghai-Tibet Plateau(QTP).Moreover,the possible influencing factors on spatiotemporal scale effect,including spatial heterogeneity,topography,and vegetation types,were explored.The results indicate that the spatial scale effect depends more on the dataset with a coarser spatial resolution,and temporal scale effects depend on the time span of datasets.Unexpectedly,the trend estimates on the 8-day and yearly scale are much closer than that on the monthly scale.In addition,in areas with low spatial heterogeneity,low topography variability,and sparse vegetation,the spatiotemporal scale effect can be ignored,and vice versa.The results in this study help deepen the consciousness and understanding of spatiotemporal scale effects on trend detection.展开更多
This paper is concerned with the initial-boundary value problem for damped wave equations with a nonlinear convection term in the multi-dimensional half space R n ＋ ： u tt u ＋ u t ＋ divf （u） = 0, t 〉 0, x = （x...This paper is concerned with the initial-boundary value problem for damped wave equations with a nonlinear convection term in the multi-dimensional half space R n ＋ ： u tt u ＋ u t ＋ divf （u） = 0, t 〉 0, x = （x 1 , x ′ ） ∈ R n ＋ ：= R ＋ × R n 1 , u（0, x） = u 0 （x） → u ＋ , as x 1 → ＋ ∞ , u t （0, x） = u 1 （x）, u（t, 0, x ′ ） = u b , x ′ = （x 2 , x 3 , ··· , x n ） ∈ R n 1 . （I） For the non-degenerate case f ′ 1 （u ＋ ） 〈 0, it was shown in [10] that the above initialboundary value problem （I） admits a unique global solution u（t, x） which converges to the corresponding planar stationary wave φ（x 1 ） uniformly in x 1 ∈ R ＋ as time tends to infinity provided that the initial perturbation and/or the strength of the stationary wave are sufficiently small. And in [10] Ueda, Nakamura, and Kawashima proved the algebraic decay estimates of the tangential derivatives of the solution u（t, x） for t → ＋ ∞ by using the space-time weighted energy method initiated by Kawashima and Matsumura [5] and improved by Nishihkawa [7]. Moreover, by using the same weighted energy method, an additional algebraic convergence rate in the normal direction was obtained by assuming that the initial perturbation decays algebraically. We note, however, that the analysis in [10] relies heavily on the assumption that f ′ （u） 〈 0. The main purpose of this paper isdevoted to discussing the case of f ′ 1 （u b ） ≥ 0 and we show that similar results still hold for such a case. Our analysis is based on some delicate energy estimates.展开更多
基金supported by the NSFC(12071437)the National Key R&D Program of China(2022YFA1005700).
文摘Combining TT* argument and bilinear interpolation,this paper obtains the Strichartz and smoothing estimates of dispersive semigroup e^(-itP(D)) in weighted L^(2) spaces.Among other things,we recover the results in[1].Moreover,the application of these results to the well-posedness of some equations are shown in the last section.
基金supported by the National Natural Science Foundation of China(NSFC,grant number U2039207).
文摘Earthquakes can cause significant damage and loss of life,necessitating immediate assessment of the resulting fatalities.Rapid assessment and timely revision of fatality estimates are crucial for effective emergency decisionmaking.This study using the February 6,2023,M_(S)8.0 and M_(S)7.9 Kahramanmaras,Türkiye earthquakes as an example to estimate the ultimate number of fatalities.An early Quick Rough Estimate(QRE)based on the number of deaths reported by the Disaster and Emergency Management Presidency of Türkiye(AFAD)is conducted,and it dynamically adjusts these estimates as new data becomes available.The range of estimates of the final number of deaths can be calculated as 31384–56475 based on the"the QRE of the second day multiplied by 2–3" rule,which incorporates the reported final deaths 50500.The Quasi-Linear and Adaptive Estimation(QLAE)method adaptively adjusts the final fatality estimate within two days and predicts subsequent reported deaths.The correct order of magnitude of the final death toll can be estimated as early as 13 hr after the M_(S)8.0 earthquake.In addition,additional earthquakes such as May 12,2008,M_(S)8.1 Wenchuan earthquake(China),September 8,2023,M_(S)7.2 Al Haouz earthquake(Morocco),November 3,2023,M_(S)5.8 Mid-Western Nepal earthquake,December 18,2023,M_(S)6.1 Jishishan earthquake(China),January 1,2024,M_(S)7.2 Noto Peninsula earthquake(Japan)and August 8,2023,Maui,Hawaii,fires are added again to verified the correctness of the model.The fatalities from the Maui fires are found to be approximately equivalent to those resulting from an M_(S)7.4 earthquake.These methods complement existing frameworks such as Quake Loss Assessment for Response and Mitigation(QLARM)and Prompt Assessment of Global.
基金supported by the National Natural Science Foundation of China(No.11971157).
文摘In this paper, we derive the a priori estimates for a class of more general (k, l)-Hessian quotient type equations involving u and Du on the right hand function. As an application we prove the Liouville theorem depending on Pogorelov type estimates. On the other hand, we obtain the existence and uniqueness of the k-admissible solution for these general equations with the Neumann boundary condition, based on some growth conditions for the right hand function.
基金Supported by the National Natural Science Foundation of China (Grant Nos.1236108412001130)。
文摘This paper is devoted to the Polynomial Preserving Recovery (PPR) based a posteriori error analysis for the second-order elliptic non-symmetric eigenvalue problem. An asymptotically exact a posteriori error estimator is proposed for solving the convection-dominated non-symmetric eigenvalue problem with non-smooth eigenfunctions or multiple eigenvalues. Numerical examples confirm our theoretical analysis.
文摘In this article,we are concerned with the C^(2)estimates for the k-convex solutions of a class of degenerate k-Hessian equations on closed Hermitian manifolds,whose function in the right-hand side is relevant to the unknown function and its gradient.We will get C^(0)estimate by promoting others′results,and get the“HMW estimate”of this equation such that the conditions of using blow-up analysis are satisfied,and the gradient estimate and second-order estimate will be obtained.Such an estimate will be helpful to study the existence for the solution of the equation.
基金Supported by NSFC(Nos.12371051,12141101,11871126)。
文摘In this paper,we study and characterize the volume estimates of geodesic balls on Finsler gradient Ricci solitons.We get the upper bounds on the volumes of geodesic balls of all three kinds of Finsler gradient Ricci solitons under certain condition about the Laplacian of thedistance function.
基金supported by the National Key Research and Development Program of China (2023YFD1902703)the National Natural Science Foundation of China (Key Program) (U23A20158)。
文摘Cropland nitrate leaching is the major nitrogen(N) loss pathway, and it contributes significantly to water pollution. However, cropland nitrate leaching estimates show great uncertainty due to variations in input datasets and estimation methods. Here, we presented a re-evaluation of Chinese cropland nitrate leaching, and identified and quantified the sources of uncertainty by integrating three cropland area datasets, three N input datasets, and three estimation methods. The results revealed that nitrate leaching from Chinese cropland averaged 6.7±0.6 Tg N yr^(-1)in 2010, ranging from 2.9 to 15.8 Tg N yr^(-1)across 27 different estimates. The primary contributor to the uncertainty was the estimation method, accounting for 45.1%, followed by the interaction of N input dataset and estimation method at 24.4%. The results of this study emphasize the need for adopting a robust estimation method and improving the compatibility between the estimation method and N input dataset to effectively reduce uncertainty. This analysis provides valuable insights for accurately estimating cropland nitrate leaching and contributes to ongoing efforts that address water pollution concerns.
基金part of the project“Qualitative and numerical analyses of some thermomechanics problems(ACUANUTER)”(Ref.PID2024-156827NB-I00)。
文摘We consider the space and time decays of certain problems within the second gradient thermal law.Notably,for this thermal theory,the exponential time decay is precluded.First,the time estimates of polynomial type are obtained for both the thermal equation and the one-dimensional thermoelastic system,where the impossibility of localization with respect to time is also established.Then,the space estimates are deduced for the multidimensional thermoelastic problem,which allow to show the exponential decay of the energy.
基金supported by the Natural Science Research Project of Anhui Educational Committee(2023AH040155)Zhisu Liu's research was supported by the Guangdong Basic and Applied Basic Research Foundation(2023A1515011679+2 种基金2024A1515012704)the Fundamental Research Funds for the Central Universities,China University of Geosciences(Wuhan)(CUG2106211CUGST2).
文摘The paper is concerned with a class of elliptic equation with critical exponent and Dipole potential.More precisely,we make use of the refined Sobolev inequality with Morrey norm to obtain the existence and decay properties of nonnegative radial ground state solutions.
基金Supported by the National Natural Science Foundation of China(Grant No.11571181)the Research Start-Up Foundation of Nantong University(Grant No.135423602051).
文摘In this paper,we give improved error estimates for linearized and nonlinear CrankNicolson type finite difference schemes of Ginzburg-Landau equation in two dimensions.For linearized Crank-Nicolson scheme,we use mathematical induction to get unconditional error estimates in discrete L^(2)and H^(1)norm.However,it is not applicable for the nonlinear scheme.Thus,based on a‘cut-off’function and energy analysis method,we get unconditional L^(2)and H^(1)error estimates for the nonlinear scheme,as well as boundedness of numerical solutions.In addition,if the assumption for exact solutions is improved compared to before,unconditional and optimal pointwise error estimates can be obtained by energy analysis method and several Sobolev inequalities.Finally,some numerical examples are given to verify our theoretical analysis.
基金Supported by the Zhejiang Provincial Natural Science Foundation of China(Grant Nos.LY20A010010,LY20A010011)the National Natural Science Foundation of China(Grant No.11971251)K.C.Wong Magna Fund in Ningbo University。
文摘In this paper,the higher order asymptotic behaviors of boundary blow-up solutions to the equation■in bounded smooth domain■are systematically investigated for p and q.The second and third order boundary behaviours of the equation are derived.The results show the role of the mean curvature of the boundary■and its gradient in the high order asymptotic expansions of the solutions.
基金Supported by the National Natural Science Foundation of China (10601022)Natural Science Foundation of Inner Mongolia Autonomous Region (200607010106)Youth Science Foundation of Inner Mongolia University(ND0702)
文摘An H^1-Galerkin mixed finite element method is discussed for a class of second order SchrSdinger equation. Optimal error estimates of semidiscrete schemes are derived for problems in one space dimension. At the same time, optimal error estimates are derived for fully discrete schemes. And it is showed that the H1-Galerkin mixed finite element approximations have the same rate of convergence as in the classical mixed finite element methods without requiring the LBB consistency condition.
基金funded by National Natural Science Foundation of China (Grant Nos. 40975013 and 40975014)Chinese Academy of Meteorological Sciences (CAMS) basic scientific and operational project:Observation and retrieval methods of microphysics and dynamic parameters of cloud and precipitation with multi-wavelength Remote Sensing,SCHeREX and TWPOR
文摘A mobile C-band dual polarimetric weather radar J type （PCDJ）, which adopts simultaneous transmission and simultaneous reception （STSR） of horizontally and vertically polarized signals, was first developed in China in 2008. It was deployed in the radar observation plan in the South China Heavy Rainfall Experiment （SCHeREX） in the summer of 2008 and 2009, as well as in Tropical Western Pacific Ocean Observation Experiments and Research on the Predictability of High Impact Weather Events from 2008 to 2010 in China （TWPOR）. Using the observation data collected in these experiments, the radar systematic error and its sources were analyzed in depth. Meanwhile an algorithm that can smooth differential propagation phase （~Dp） for estimating the high-resolution specific differential phase （KDP） was developed. After attenuation correction of reflectivity in horizontal polarization （ZH） and differential reflectivity （ZDR） of PCDJ radar by means of KDP, the data quality was improved significantly. Using quality-controlled radar data, quantitative rainfall estimation was performed, and the resutls were compared with rain-gauge measurements. A synthetic ZH /KDp-based method was analyzed. The results the traditional ZH-based method when the rain suggest that the synthetic method has the advantage over rate is 〉5 mm h^-1. The more intensive the rain rates, the higher accuracy of the estimation.
基金Projects(41820104005,41904004,42030112)supported by the National Natural Science Foundation of China。
文摘The Ice,Cloud and Land Elevation Satellite-2(ICESat-2),a new spaceborne light detection and ranging(LiDAR)system,was successfully launched on September 15,2018.The ICESat-2 data increase the types of spaceborne LiDAR data archive and provide new control point data for large-scale topographic mapping and geodetic surveying.However,the accuracy of the ATL 08 terrain estimates has not been fully evaluated on a large scale and in complex terrain conditions.This article aims to quantitatively assess the accuracy of ICESat-2 ATL 08 terrain estimates.Firstly,the ICESat-2 ATL 08 terrain estimates were compared with the high-precision airborne LiDAR digital terrain model(DTM),and impacts of acquisition time,vegetation cover type,terrain slope,and season change on the terrain estimation accuracy were analyzed.We get the following conclusions from the analysis:1)the mean and RMSE of the terrain estimates of day acquisitions are 0.22 m and 0.59 m higher than that of night acquisitions;2)the accuracy of the ATL 08 terrain estimates acquired in vegetated areas is lower than those in non-vegetated areas;3)the accuracy of the ATL 08 terrain estimates is inversely proportional to the slope,and the elevation error increases significantly when the terrain slope is larger than 30°;4)in the non-vegetation covered area,the accuracy of the ATL 08 terrain estimates of summer and winter acquisitions has no obvious discrepancy,but in vegetated area,the accuracy of winter acquisitions is significantly better than that of summer acquisitions.This research provides references for the selection and application of ICESat-2 data.
基金National Key R&D Program of China(No.2016YFA0601601)National Natural Science Foundation of China(No.41601026,41661099)Science and Technology Planning Project of Yunnan Province,China(No.2017FB073)
文摘Satellite-based products with high spatial and temporal resolution provide useful precipitation information for data-sparse or ungauged large-scale watersheds. In the Lower Lancang-Mekong River Basin, rainfall stations are sparse and unevenly distributed, and the transboundary characteristic makes the collection of precipitation data more difficult, which has restricted hydrological processes simulation. In this study, daily precipitation data from four datasets(gauge observations, inverse distance weighted(IDW) data, Tropical Rainfall Measuring Mission(TRMM) estimates, and Climate Hazards Group InfraRed Precipitation with Stations(CHIRPS) estimates), were applied to drive the Soil and Water Assessment Tool(SWAT) model, and then their capability for hydrological simulation in the Lower Lancang-Mekong River Basin were examined. TRMM and CHIRPS data showed good performances on precipitation estimation in the Lower Lancang-Mekong River Basin, with the better performance for TRMM product. The Nash-Sutcliffe efficiency(NSE) values of gauge, IDW, TRMM, and CHIRPS simulations during the calibration period were 0.87, 0.86, 0.95, and 0.93 for monthly flow, respectively, and those for daily flow were 0.75, 0.77, 0.86, and 0.84, respectively. TRMM and CHIRPS data were superior to rain gauge and IDW data for driving the hydrological model, and TRMM data produced the best simulation performance. Satellite-based precipitation estimates could be suitable data sources when simulating hydrological processes for large data-poor or ungauged watersheds, especially in international river basins for which precipitation observations are difficult to collect. CHIRPS data provide long precipitation time series from 1981 to near present and thus could be used as an alternative precipitation input for hydrological simulation, especially for the period without TRMM data. For satellite-based precipitation products, the differences in the occurrence frequencies and amounts of precipitation with different intensities would affect simulation results of water balance components, which should be comprehensively considered in water resources estimation and planning.
基金Supported by the National Natural Science Foundation of China(10976026)the Fujian Provincial Department of Science and Technology(JK2009045)
文摘In this paper, under the hypothesis that y is upper bounded, we construct a Lyapunov functional for the multidimensional isentropic compressible magnetohydrodynamic equations and show that the weak solutions decay exponentially to the equilibrium state in L2 norm. Our result verifies that the method of Daoyuan Fang, Ruizhao Zi and Ting Zhang I1] can be adapted to magnetohydrodynamic equations.
基金supported by the Fundamental Research Fund for the Central Universities
文摘Let （M,g, e^-fdv） be a smooth metric measure space. In this paper, we con- sider two nonlinear weighted p-heat equations. Firstly, we derive a Li-Yau type gradient estimates for the positive solutions to the following nonlinear weighted p-heat equationand f is a smooth function on M under the assumptionthat the m-dimensional nonnegative Bakry-Emery Ricci curvature. Secondly, we show an entropy monotonicity formula with nonnegative m-dimensional Bakry-Emery Ricci curva- ture which is a generalization to the results of Kotschwar and Ni [9], Li [7].
基金The research was supported by the Natural Science Foundation of China
文摘A nonlinear parabolic system is derived to describe incompressible nuclear waste-disposal contamination in porous media. A sequential implicit tirne-stepping is defined, in which the pressure and Darcy velocity of the mixture are approximated simultaneously by a mixed finite element method and the brine, radionuclid and heat are treated by a combination of a Galerkin finite element method and the method of characteristics. Optimal-order convergence in L2 is proved. Time-truncation errors of standard procedures are reduced by time stepping along the characteristics of the hyperbolic part of the brine, radionuclide and heal equalios, temporal and spatial error are lossened by direct compulation of the velocity in the mixed method, as opposed to differentiation of the pressure.
基金The Second Tibetan Plateau Scientific Expedition and Research Program(STEP),No.2019QZKK0605National Natural Science Foundation of China,No.42071296。
文摘The trend estimate of vegetation change is essential to understand the change rule of the ecosystem.Previous studies were mainly focused on quantifying trends or analyzing their spatial distribution characteristics.Nevertheless,the uncertainties of trend estimates caused by spatiotemporal scale effects have rarely been studied.In response to this challenge,this study aims to investigate spatiotemporal scale effects on trend estimates using Moderate-Resolution Imaging Spectroradiometer(MODIS)Normalized Difference Vegetation Index(NDVI)and Gross Primary Productivity(GPP)products from 2001 to 2019 in the Qinghai-Tibet Plateau(QTP).Moreover,the possible influencing factors on spatiotemporal scale effect,including spatial heterogeneity,topography,and vegetation types,were explored.The results indicate that the spatial scale effect depends more on the dataset with a coarser spatial resolution,and temporal scale effects depend on the time span of datasets.Unexpectedly,the trend estimates on the 8-day and yearly scale are much closer than that on the monthly scale.In addition,in areas with low spatial heterogeneity,low topography variability,and sparse vegetation,the spatiotemporal scale effect can be ignored,and vice versa.The results in this study help deepen the consciousness and understanding of spatiotemporal scale effects on trend detection.
基金The research of Fan Lili was supported by two grants from the National Natural Science Foundation of China (10871151 10925103)+1 种基金the research of Liu Hongxia was supported by National Natural Science Foundation of China (10871082)the research of Yin Hui was supported by National Natural Sciences Foundation of China (10901064)
文摘This paper is concerned with the initial-boundary value problem for damped wave equations with a nonlinear convection term in the multi-dimensional half space R n ＋ ： u tt u ＋ u t ＋ divf （u） = 0, t 〉 0, x = （x 1 , x ′ ） ∈ R n ＋ ：= R ＋ × R n 1 , u（0, x） = u 0 （x） → u ＋ , as x 1 → ＋ ∞ , u t （0, x） = u 1 （x）, u（t, 0, x ′ ） = u b , x ′ = （x 2 , x 3 , ··· , x n ） ∈ R n 1 . （I） For the non-degenerate case f ′ 1 （u ＋ ） 〈 0, it was shown in [10] that the above initialboundary value problem （I） admits a unique global solution u（t, x） which converges to the corresponding planar stationary wave φ（x 1 ） uniformly in x 1 ∈ R ＋ as time tends to infinity provided that the initial perturbation and/or the strength of the stationary wave are sufficiently small. And in [10] Ueda, Nakamura, and Kawashima proved the algebraic decay estimates of the tangential derivatives of the solution u（t, x） for t → ＋ ∞ by using the space-time weighted energy method initiated by Kawashima and Matsumura [5] and improved by Nishihkawa [7]. Moreover, by using the same weighted energy method, an additional algebraic convergence rate in the normal direction was obtained by assuming that the initial perturbation decays algebraically. We note, however, that the analysis in [10] relies heavily on the assumption that f ′ （u） 〈 0. The main purpose of this paper isdevoted to discussing the case of f ′ 1 （u b ） ≥ 0 and we show that similar results still hold for such a case. Our analysis is based on some delicate energy estimates.
