This paper is concerned with the dissipation of solutions of the isentropic Navier-Stokes equations in even and bigger than two multi-dimensions. Pointwise estimates of the time-asymptotic shape of the solutions are o...This paper is concerned with the dissipation of solutions of the isentropic Navier-Stokes equations in even and bigger than two multi-dimensions. Pointwise estimates of the time-asymptotic shape of the solutions are obtained and the generalized Huygan's principle is exhibited. The approch of the paper is based on the detailed analysis of the Green function of Iinearized system. This is used to study the coupling of nonlinear diffesion waves.展开更多
This paper studies the time asymptotic behavior of solutions for a nonlinear convection diffusion reaction equation in one dimension.First,the pointwise estimates of solutions are obtained,furthermore,we obtain the op...This paper studies the time asymptotic behavior of solutions for a nonlinear convection diffusion reaction equation in one dimension.First,the pointwise estimates of solutions are obtained,furthermore,we obtain the optimal Lp,1≤ p ≤ ＋∞,convergence rate of solutions for small initial data.Then we establish the local existence of solutions,the blow up criterion and the sufficient condition to ensure the nonnegativity of solutions for large initial data.Our approach is based on the detailed analysis of the Green function of the linearized equation and some energy estimates.展开更多
In this article,we study the pointwise estimates of solutions to the nonlinear viscous wave equation in even dimensions(n≥4).We use the Green’s function method.Our approach is on the basis of the detailed analysis o...In this article,we study the pointwise estimates of solutions to the nonlinear viscous wave equation in even dimensions(n≥4).We use the Green’s function method.Our approach is on the basis of the detailed analysis of the Green’s function of the linearized system.We show that the decay rates of the solution for the same problem are different in even dimensions and odd dimensions.It is shown that the solution exhibits a generalized Huygens principle.展开更多
This paper is devoted to the pointwise estimate of solutions for the initial value problem to the three-dimensional compressible magnetohydrodynamic equations, which models the dynamics of compressible quasi-neutrally...This paper is devoted to the pointwise estimate of solutions for the initial value problem to the three-dimensional compressible magnetohydrodynamic equations, which models the dynamics of compressible quasi-neutrally ionized fluids under the influence of electromagnetic fields. Based on the detailed analysis of the Green function of the linearized system, we obtain the pointwise estimates of smooth solutions when the initial data is sufficiently small with the algebraic decay to the constant equilibrium. As the by-product, we also show the corresponding pL-estimates of the smooth solutions.展开更多
In this paper, we study the linear thermo-visco-elastic system in one-dimensional space variable. The mathematical model is a hyperbolic-parabolic partial differential system. The solutions of the system show some dec...In this paper, we study the linear thermo-visco-elastic system in one-dimensional space variable. The mathematical model is a hyperbolic-parabolic partial differential system. The solutions of the system show some decay property due to the parabolicity. Based on detailed analysis on the Green function of the system, the pointwise estimates of the solutions are obtained, from which the generalized Huygens’ principle is shown.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
For linear combinations of Gamma operators, if 0<a<2r, 1/2-1/2r≤λ≤1. or 0≤λ≤1/2-1/2r(r≥2),0 <a<r+1/1-λ, we obtain an equivalent theorem with ω(?)(f,t) instead of ω(?)(f,t), where ω(?)(f,t) is th...For linear combinations of Gamma operators, if 0<a<2r, 1/2-1/2r≤λ≤1. or 0≤λ≤1/2-1/2r(r≥2),0 <a<r+1/1-λ, we obtain an equivalent theorem with ω(?)(f,t) instead of ω(?)(f,t), where ω(?)(f,t) is the Ditzian-Totik moduli of smoothness.展开更多
The Cauchy problem of the generalized Kuramoto-Sivashinsky equation in multidimensions(n ≥ 3) is considered. Based on Green's function method, some ingenious energy estimates are given. Then the global existence ...The Cauchy problem of the generalized Kuramoto-Sivashinsky equation in multidimensions(n ≥ 3) is considered. Based on Green's function method, some ingenious energy estimates are given. Then the global existence and pointwise convergence rates of the classical solutions are established. Furthermore, the L^p convergence rate of the solution is obtained.展开更多
This paper research on the pointwise behavior of perturbations from a viscous shock solution to a scalar viscous conservation law by introducing an approximate Green’s function. The authors obtain not only the pointw...This paper research on the pointwise behavior of perturbations from a viscous shock solution to a scalar viscous conservation law by introducing an approximate Green’s function. The authors obtain not only the pointwise decay of the perturbation and but also the high derivative of it. Stability in anyL(p≥1) norm is a direct consequence.展开更多
In this paper we focus on the initial value problem of a hyperbolic-elliptic coupled system in multi-dimensional space of a radiating gas. By using the method of Green function combined with Fourier analysis, we obtai...In this paper we focus on the initial value problem of a hyperbolic-elliptic coupled system in multi-dimensional space of a radiating gas. By using the method of Green function combined with Fourier analysis, we obtain the pointwise decay estimates of solutions to the problem.展开更多
Cauchy problem of Cahn-Hilliard equation with inertial term in three-dimensional space is considered.Using delicate analysis of its Green function and its convolution with nonlinear term,pointwise decay rate is obtained.
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
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
In this paper,we study the nonlinear stability problem for the two-dimensional Boussinesq system around the Couette flow in a finite channel with Navier-slip boundary condition for the velocity and Dirichlet boundary ...In this paper,we study the nonlinear stability problem for the two-dimensional Boussinesq system around the Couette flow in a finite channel with Navier-slip boundary condition for the velocity and Dirichlet boundary condition for the temperature with small viscosityνand small thermal diffusionμ.We establish that if the initial perturbation velocity and initial perturbation temperature satisfy ||u_(0)||H^(2)≤ε_(0) min{μ,ν}1/2, and ||θ_(0)||H^(1)+|||D_(x)|^(1/3)θ_(0)||H^(1)+|||D_(x)|^(1/3)θ_(0)||_(H^(1))≤εi min{μ,ν}^(5/6),for some smallε0 andε1 independent ofμ,ν,then the solution of the two-dimensional NavierStokes Boussinesq system does not transition away from the Couette flow for any time.展开更多
Recognizing discontinuities within rock masses is a critical aspect of rock engineering.The development of remote sensing technologies has significantly enhanced the quality and quantity of the point clouds collected ...Recognizing discontinuities within rock masses is a critical aspect of rock engineering.The development of remote sensing technologies has significantly enhanced the quality and quantity of the point clouds collected from rock outcrops.In response,we propose a workflow that balances accuracy and efficiency to extract discontinuities from massive point clouds.The proposed method employs voxel filtering to downsample point clouds,constructs a point cloud topology using K-d trees,utilizes principal component analysis to calculate the point cloud normals,and employs the pointwise clustering(PWC)algorithm to extract discontinuities from rock outcrop point clouds.This method provides information on the location and orientation(dip direction and dip angle)of the discontinuities,and the modified whale optimization algorithm(MWOA)is utilized to identify major discontinuity sets and their average orientations.Performance evaluations based on three real cases demonstrate that the proposed method significantly reduces computational time costs without sacrificing accuracy.In particular,the method yields more reasonable extraction results for discontinuities with certain undulations.The presented approach offers a novel tool for efficiently extracting discontinuities from large-scale point clouds.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
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
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
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
基金Supported in part by National Natural Science Foundationof China (19871065) Hua-Cheng Grant
文摘This paper is concerned with the dissipation of solutions of the isentropic Navier-Stokes equations in even and bigger than two multi-dimensions. Pointwise estimates of the time-asymptotic shape of the solutions are obtained and the generalized Huygan's principle is exhibited. The approch of the paper is based on the detailed analysis of the Green function of Iinearized system. This is used to study the coupling of nonlinear diffesion waves.
文摘This paper studies the time asymptotic behavior of solutions for a nonlinear convection diffusion reaction equation in one dimension.First,the pointwise estimates of solutions are obtained,furthermore,we obtain the optimal Lp,1≤ p ≤ ＋∞,convergence rate of solutions for small initial data.Then we establish the local existence of solutions,the blow up criterion and the sufficient condition to ensure the nonnegativity of solutions for large initial data.Our approach is based on the detailed analysis of the Green function of the linearized equation and some energy estimates.
文摘In this article,we study the pointwise estimates of solutions to the nonlinear viscous wave equation in even dimensions(n≥4).We use the Green’s function method.Our approach is on the basis of the detailed analysis of the Green’s function of the linearized system.We show that the decay rates of the solution for the same problem are different in even dimensions and odd dimensions.It is shown that the solution exhibits a generalized Huygens principle.
基金Supported by Research Grant of Department of Education of Hubei Province(Q20142803)
文摘This paper is devoted to the pointwise estimate of solutions for the initial value problem to the three-dimensional compressible magnetohydrodynamic equations, which models the dynamics of compressible quasi-neutrally ionized fluids under the influence of electromagnetic fields. Based on the detailed analysis of the Green function of the linearized system, we obtain the pointwise estimates of smooth solutions when the initial data is sufficiently small with the algebraic decay to the constant equilibrium. As the by-product, we also show the corresponding pL-estimates of the smooth solutions.
基金Xingwen Hao's research was supported in part by National Natural Science Foundation of China (10571120 and 10971135)Shanghai Shuguang Project (06SG11)+1 种基金the Program for New Century Excellent Talents of Chinese Ministry of Education (NCET-07-0546) Doctorial Foundation of Weifang University (2011BS11)
文摘In this paper, we study the linear thermo-visco-elastic system in one-dimensional space variable. The mathematical model is a hyperbolic-parabolic partial differential system. The solutions of the system show some decay property due to the parabolicity. Based on detailed analysis on the Green function of the system, the pointwise estimates of the solutions are obtained, from which the generalized Huygens’ principle is shown.
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 Hebei Provincial Natural Science Foundation of China(101090). Supported by the Major Subject Foundation of Hebei Normal University.
文摘For linear combinations of Gamma operators, if 0<a<2r, 1/2-1/2r≤λ≤1. or 0≤λ≤1/2-1/2r(r≥2),0 <a<r+1/1-λ, we obtain an equivalent theorem with ω(?)(f,t) instead of ω(?)(f,t), where ω(?)(f,t) is the Ditzian-Totik moduli of smoothness.
基金supported by the National Natural Science Foundation of China(11271141)Chongqing Science&Technology Commission(cstc2018jcyjAX0787)
文摘The Cauchy problem of the generalized Kuramoto-Sivashinsky equation in multidimensions(n ≥ 3) is considered. Based on Green's function method, some ingenious energy estimates are given. Then the global existence and pointwise convergence rates of the classical solutions are established. Furthermore, the L^p convergence rate of the solution is obtained.
基金the National Natural Science Foundation of China(10131050)
文摘This paper research on the pointwise behavior of perturbations from a viscous shock solution to a scalar viscous conservation law by introducing an approximate Green’s function. The authors obtain not only the pointwise decay of the perturbation and but also the high derivative of it. Stability in anyL(p≥1) norm is a direct consequence.
文摘In this paper we focus on the initial value problem of a hyperbolic-elliptic coupled system in multi-dimensional space of a radiating gas. By using the method of Green function combined with Fourier analysis, we obtain the pointwise decay estimates of solutions to the problem.
基金Supported by the National Natural Science Foundation of China(11801137)。
文摘Cauchy problem of Cahn-Hilliard equation with inertial term in three-dimensional space is considered.Using delicate analysis of its Green function and its convolution with nonlinear term,pointwise decay rate is obtained.
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 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.
文摘In this paper,we study the nonlinear stability problem for the two-dimensional Boussinesq system around the Couette flow in a finite channel with Navier-slip boundary condition for the velocity and Dirichlet boundary condition for the temperature with small viscosityνand small thermal diffusionμ.We establish that if the initial perturbation velocity and initial perturbation temperature satisfy ||u_(0)||H^(2)≤ε_(0) min{μ,ν}1/2, and ||θ_(0)||H^(1)+|||D_(x)|^(1/3)θ_(0)||H^(1)+|||D_(x)|^(1/3)θ_(0)||_(H^(1))≤εi min{μ,ν}^(5/6),for some smallε0 andε1 independent ofμ,ν,then the solution of the two-dimensional NavierStokes Boussinesq system does not transition away from the Couette flow for any time.
基金supported by the National Natural Science Foundation of China(Grant No.42407232)the Sichuan Science and Technology Program(Grant No.2024NSFSC0826).
文摘Recognizing discontinuities within rock masses is a critical aspect of rock engineering.The development of remote sensing technologies has significantly enhanced the quality and quantity of the point clouds collected from rock outcrops.In response,we propose a workflow that balances accuracy and efficiency to extract discontinuities from massive point clouds.The proposed method employs voxel filtering to downsample point clouds,constructs a point cloud topology using K-d trees,utilizes principal component analysis to calculate the point cloud normals,and employs the pointwise clustering(PWC)algorithm to extract discontinuities from rock outcrop point clouds.This method provides information on the location and orientation(dip direction and dip angle)of the discontinuities,and the modified whale optimization algorithm(MWOA)is utilized to identify major discontinuity sets and their average orientations.Performance evaluations based on three real cases demonstrate that the proposed method significantly reduces computational time costs without sacrificing accuracy.In particular,the method yields more reasonable extraction results for discontinuities with certain undulations.The presented approach offers a novel tool for efficiently extracting discontinuities from large-scale point clouds.
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 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.
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.
