In this paper,we consider the fourth-order parabolic equation with p(x)Laplacian and variable exponent source ut+∆^(2)u−div(|■u|^(p(x)−2■u))=|u|^(q(x))−1u.By applying potential well method,we obtain global existence...In this paper,we consider the fourth-order parabolic equation with p(x)Laplacian and variable exponent source ut+∆^(2)u−div(|■u|^(p(x)−2■u))=|u|^(q(x))−1u.By applying potential well method,we obtain global existence,asymptotic behavior and blow-up of solutions with initial energy J(u_(0))≤d.Moreover,we estimate the upper bound of the blow-up time for J(u_(0))≤0.展开更多
This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic diff...This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic differential equations.Then we obtain a comparison theorem in one-dimensional situation.展开更多
In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to ...In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.展开更多
The existence of a global attractor is established for generalized Navier-Stokes equations incorporating damping term within the periodic domainΩ=[−π,π]^(n).Initially,we show the existence and uniqueness of strong ...The existence of a global attractor is established for generalized Navier-Stokes equations incorporating damping term within the periodic domainΩ=[−π,π]^(n).Initially,we show the existence and uniqueness of strong solutions.Subsequently,we verify the continuity of the associated semigroup when max■.Finally,we establish the existence of both H^(α)-global attractor and H^(2α)-global attractor.展开更多
The goal of this paper is to investigate the long-time dynamics of solutions to a Kirchhoff type suspension bridge equation with nonlinear damping and memory term.For this problem we establish the well-posedness and e...The goal of this paper is to investigate the long-time dynamics of solutions to a Kirchhoff type suspension bridge equation with nonlinear damping and memory term.For this problem we establish the well-posedness and existence of uniform attractor under some suitable assumptions on the nonlinear term g(u),the nonlinear damping f(u_(t))and the external force h(x,t).Specifically,the asymptotic compactness of the semigroup is verified by the energy reconstruction method.展开更多
A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue prob...A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue problem,the method is spectral-correct and spurious-free.Stability and error estimates are obtained,including the interpolation error estimates and the error estimates between the finite element solution and the exact solution.The method is suitable for singular solution as well as smooth solution,and consequently,the method is valid for nonconvex domains which may have a number of reentrant corners.Of course,the method is suitable for arbitrary quadrilaterals(under the usual shape-regular condition).展开更多
We investigate the constrained fractional Choquard equation■where m>0,N>2s with s∈(0,1)being the order of the fractional Laplacian operator and I_(α)forα∈(0,N)denotes the Riesz potential.The parameterμ∈ℝa...We investigate the constrained fractional Choquard equation■where m>0,N>2s with s∈(0,1)being the order of the fractional Laplacian operator and I_(α)forα∈(0,N)denotes the Riesz potential.The parameterμ∈ℝappears as a Lagrange multiplier.By imposing general mass-supercritical conditions on F,we confirm the existence of normalized solutions that characterize the global minimizer on the Pohozaev manifold.Our proof does not depend on the assumption that all weak solutions satisfy the Pohozaev identity,a challenge that remains unsolved for this doubly nonlocal equation.展开更多
In this paper,we present a finite volume trigonometric weighted essentially non-oscillatory(TWENO)scheme to solve nonlinear degenerate parabolic equations that may exhibit non-smooth solutions.The present method is de...In this paper,we present a finite volume trigonometric weighted essentially non-oscillatory(TWENO)scheme to solve nonlinear degenerate parabolic equations that may exhibit non-smooth solutions.The present method is developed using the trigonometric scheme,which is based on zero,first,and second moments,and the direct discontinuous Galerkin(DDG)flux is used to discretize the diffusion term.Moreover,the DDG method directly applies the weak form of the parabolic equation to each computational cell,which can better capture the characteristics of the solution,especially the discontinuous solution.Meanwhile,the third-order TVD-Runge-Kutta method is applied for temporal discretization.Finally,the effectiveness and stability of the method constructed in this paper are evaluated through numerical tests.展开更多
AIM:To build a functional generalized estimating equation(GEE)model to detect glaucomatous visual field progression and compare the performance of the proposed method with that of commonly employed algorithms.METHODS:...AIM:To build a functional generalized estimating equation(GEE)model to detect glaucomatous visual field progression and compare the performance of the proposed method with that of commonly employed algorithms.METHODS:Totally 716 eyes of 716 patients with primary open angle glaucoma(POAG)with at least 5 reliable 24-2 test results and 2y of follow-up were selected.The functional GEE model was used to detect perimetric progression in the training dataset(501 eyes).In the testing dataset(215 eyes),progression was evaluated the functional GEE model,mean deviation(MD)and visual field index(VFI)rates of change,Advanced Glaucoma Intervention Study(AGIS)and Collaborative Initial Glaucoma Treatment Study(CIGTS)scores,and pointwise linear regression(PLR).RESULTS:The proposed method showed the highest proportion of eyes detected as progression(54.4%),followed by the VFI rate(34.4%),PLR(23.3%),and MD rate(21.4%).The CIGTS and AGIS scores had a lower proportion of eyes detected as progression(7.9%and 5.1%,respectively).The time to detection of progression was significantly shorter for the proposed method than that of other algorithms(adjusted P≤0.019).The VFI rate displayed moderate pairwise agreement with the proposed method(k=0.47).CONCLUSION:The functional GEE model shows the highest proportion of eyes detected as perimetric progression and the shortest time to detect perimetric progression in patients with POAG.展开更多
Physics-informed neural networks(PINNs),as a novel artificial intelligence method for solving partial differential equations,are applicable to solve both forward and inverse problems.This study evaluates the performan...Physics-informed neural networks(PINNs),as a novel artificial intelligence method for solving partial differential equations,are applicable to solve both forward and inverse problems.This study evaluates the performance of PINNs in solving the temperature diffusion equation of the seawater across six scenarios,including forward and inverse problems under three different boundary conditions.Results demonstrate that PINNs achieved consistently higher accuracy with the Dirichlet and Neumann boundary conditions compared to the Robin boundary condition for both forward and inverse problems.Inaccurate weighting of terms in the loss function can reduce model accuracy.Additionally,the sensitivity of model performance to the positioning of sampling points varied between different boundary conditions.In particular,the model under the Dirichlet boundary condition exhibited superior robustness to variations in point positions during the solutions of inverse problems.In contrast,for the Neumann and Robin boundary conditions,accuracy declines when points were sampled from identical positions or at the same time.Subsequently,the Argo observations were used to reconstruct the vertical diffusion of seawater temperature in the north-central Pacific for the applicability of PINNs in the real ocean.The PINNs successfully captured the vertical diffusion characteristics of seawater temperature,reflected the seasonal changes of vertical temperature under different topographic conditions,and revealed the influence of topography on the temperature diffusion coefficient.The PINNs were proved effective in solving the temperature diffusion equation of seawater with limited data,providing a promising technique for simulating or predicting ocean phenomena using sparse observations.展开更多
Owing to intensified globalization and informatization,the structures of the urban scale hierarchy and urban networks between cities have become increasingly intertwined,resulting in different spatial effects.Therefor...Owing to intensified globalization and informatization,the structures of the urban scale hierarchy and urban networks between cities have become increasingly intertwined,resulting in different spatial effects.Therefore,this paper analyzes the spatial interaction between urban scale hierarchy and urban networks in China from 2019 to 2023,drawing on Baidu migration data and employing a spatial simultaneous equation model.The results reveal a significant positive spatial correlation between cities with higher hierarchy and those with greater network centrality.Within a static framework,we identify a positive interaction between urban scale hierarchy and urban network centrality,while their spatial cross-effects manifest as negative neighborhood interactions based on geographical distance and positive cross-scale interactions shaped by network connections.Within a dynamic framework,changes in urban scale hierarchy and urban networks are mutually reinforcing,thereby widening disparities within the urban hierarchy.Furthermore,an increase in a city’s network centrality had a dampening effect on the population growth of neighboring cities and network-connected cities.This study enhances understanding of the spatial organisation of urban systems and offers insights for coordinated regional development.展开更多
In order to better describe the phenomenon of biological invasion,this paper introduces a free boundary model of biological invasion.Firstly,the right free boundary is added to the equation with logistic terms.Secondl...In order to better describe the phenomenon of biological invasion,this paper introduces a free boundary model of biological invasion.Firstly,the right free boundary is added to the equation with logistic terms.Secondly,the existence and uniqueness of local solutions are proved by the Sobolev embedding theorem and the comparison principle.Finally,according to the relevant research data and contents of red fire ants,the diffusion area and nest number of red fire ants were simulated without external disturbance.This paper mainly simulates the early diffusion process of red fire ants.In the early diffusion stage,red fire ants grow slowly and then spread over a large area after reaching a certain number.展开更多
Deep neural networks(DNNs)are effective in solving both forward and inverse problems for nonlinear partial differential equations(PDEs).However,conventional DNNs are not effective in handling problems such as delay di...Deep neural networks(DNNs)are effective in solving both forward and inverse problems for nonlinear partial differential equations(PDEs).However,conventional DNNs are not effective in handling problems such as delay differential equations(DDEs)and delay integrodifferential equations(DIDEs)with constant delays,primarily due to their low regularity at delayinduced breaking points.In this paper,a DNN method that combines multi-task learning(MTL)which is proposed to solve both the forward and inverse problems of DIDEs.The core idea of this approach is to divide the original equation into multiple tasks based on the delay,using auxiliary outputs to represent the integral terms,followed by the use of MTL to seamlessly incorporate the properties at the breaking points into the loss function.Furthermore,given the increased training dificulty associated with multiple tasks and outputs,we employ a sequential training scheme to reduce training complexity and provide reference solutions for subsequent tasks.This approach significantly enhances the approximation accuracy of solving DIDEs with DNNs,as demonstrated by comparisons with traditional DNN methods.We validate the effectiveness of this method through several numerical experiments,test various parameter sharing structures in MTL and compare the testing results of these structures.Finally,this method is implemented to solve the inverse problem of nonlinear DIDE and the results show that the unknown parameters of DIDE can be discovered with sparse or noisy data.展开更多
In order to solve the problem of the variable coefficient ordinary differen-tial equation on the bounded domain,the Lagrange interpolation method is used to approximate the exact solution of the equation,and the error...In order to solve the problem of the variable coefficient ordinary differen-tial equation on the bounded domain,the Lagrange interpolation method is used to approximate the exact solution of the equation,and the error between the numerical solution and the exact solution is obtained,and then compared with the error formed by the difference method,it is concluded that the Lagrange interpolation method is more effective in solving the variable coefficient ordinary differential equation.展开更多
An equation of state(EOS)was obtained that accurately describes the thermodynamics of the system H_(2)O–CO_(2) at temperatures of 50–350°C and pressures of 0.2–3.5 kbar.The equation is based on experimental da...An equation of state(EOS)was obtained that accurately describes the thermodynamics of the system H_(2)O–CO_(2) at temperatures of 50–350°C and pressures of 0.2–3.5 kbar.The equation is based on experimental data on the compositions of the coexisting liquid and gas phases and the Van Laar model,within which the values of the Van Laar parameters A12 and A21 were found for each experimental P-T point.For the resulting sets A12(P,T),A21(P,T),approximation formulas describing the dependences of these quantities on temperature and pressure were found and the parameters contained in the formulas were fitted.This two-stage approach made it possible to obtain an adequate thermodynamic description of the system,which allows,in addition to determining the phase state of the system(homogeneous or heterogeneous),to calculate the excess free energy of mixing of H_(2)O and CO_(2),the activities of H_(2)O and CO_(2),and other thermodynamic characteristics of the system.The possibility of such calculations creates the basis for using the obtained EOS in thermodynamic models of more complicated fluid systems in P-T conditions of the middle and upper crust.These fluids play an important role in many geological processes including the transport of ore matter and forming hydrothermal ore deposits,in particular,the most of the world’s gold deposits.The knowledge of thermodynamics of these fluids is important in the technology of drilling oil and gas wells.In particular,this concerns the prevention of precipitation of solid salts in the well.展开更多
This paper deals with quasilinear elliptic equations of singular growth like-Δu-uΔ(u^(2))=a(x)u^(-1).We establish the existence of positive solutions for general a(x)∈L^(p)(Ω),p>2,whereΩis a bounded domain inℝ...This paper deals with quasilinear elliptic equations of singular growth like-Δu-uΔ(u^(2))=a(x)u^(-1).We establish the existence of positive solutions for general a(x)∈L^(p)(Ω),p>2,whereΩis a bounded domain inℝ^(N)with N≥1.展开更多
Reference crop evapotranspiration (ETo) is essential for irrigation, water resources management and environmental assessment. The indirect estimation of ETo is based a) on energy budget approach using meteorological d...Reference crop evapotranspiration (ETo) is essential for irrigation, water resources management and environmental assessment. The indirect estimation of ETo is based a) on energy budget approach using meteorological data and b) pan evaporation measurements (Epan) multiplied by pan coefficients (kp) adapted to the surrounding environmental conditions. Significant interest is shown for the kp equations, which have to be tested before their use. The purpose of this study is to evaluate six different kp equations, such as those of Cuenca, Allen and Puitt, Snyder, Pereira et al., Orang, Raghuwanshi and Wallender for the summer growing season (April to October) of Thessaloniki plain in Greece, which is characterized by a semi-arid Mediterranean environment. The evaluation of the kp equations is performed by two years Epan measurements, using as reference the daily ETo values estimated by the ASCE-standardized Penman-Monteith equation (ASCE-PM) in hourly time step. The results of this study showed that Cuenca’s equation provided more accurate daily estimations. Additional analysis is performed in other methods such as those of FAO-56 and Hargreaves based on the calculation time step (hourly or daily) and their correspondence to the ASCE-PM.展开更多
In this paper,we focus on peaked traveling wave solutions of the modified highly nonlinear Novikov equation by dynamical systems approach.We obtain a traveling wave system which is a singular planar dynamical system w...In this paper,we focus on peaked traveling wave solutions of the modified highly nonlinear Novikov equation by dynamical systems approach.We obtain a traveling wave system which is a singular planar dynamical system with three singular straight lines,and derive all possible phase portraits under corresponding parameter conditions.Then we show the existence and dynamics of two types of peaked traveling wave solutions including peakons and periodic cusp wave solutions.The exact explicit expressions of two peakons are given.Besides,we also derive smooth solitary wave solutions,periodic wave solutions,compacton solutions,and kink-like(antikink-like)solutions.Numerical simulations are further performed to verify the correctness of the results.Most importantly,peakons and periodic cusp wave solutions are newly found for the equation,which extends the previous results.展开更多
In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with ...In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with prescribed 2-norm has some normalized solutions by introducing variational methods.展开更多
This paper deals with the monotonicity of limit wave speed c0(h)to a perturbed g KdV equation.We show the decrease of c0(h)by combining the analytic method and the numerical technique.Our results solve a special case ...This paper deals with the monotonicity of limit wave speed c0(h)to a perturbed g KdV equation.We show the decrease of c0(h)by combining the analytic method and the numerical technique.Our results solve a special case of the open question presented by Yan et al.,and the method potentially provides a way to study the monotonicity of c0(h)for general m∈N^(+).展开更多
基金Supported by NSFC(No.12101482)the Natural Science Foundation of Shaanxi Province,China(No.2018JQ1052)。
文摘In this paper,we consider the fourth-order parabolic equation with p(x)Laplacian and variable exponent source ut+∆^(2)u−div(|■u|^(p(x)−2■u))=|u|^(q(x))−1u.By applying potential well method,we obtain global existence,asymptotic behavior and blow-up of solutions with initial energy J(u_(0))≤d.Moreover,we estimate the upper bound of the blow-up time for J(u_(0))≤0.
基金Supported by the National Natural Science Foundation of China(12001074)the Research Innovation Program of Graduate Students in Hunan Province(CX20220258)+1 种基金the Research Innovation Program of Graduate Students of Central South University(1053320214147)the Key Scientific Research Project of Higher Education Institutions in Henan Province(25B110025)。
文摘This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic differential equations.Then we obtain a comparison theorem in one-dimensional situation.
基金Supported in part by Natural Science Foundation of Guangxi(2023GXNSFAA026246)in part by the Central Government's Guide to Local Science and Technology Development Fund(GuikeZY23055044)in part by the National Natural Science Foundation of China(62363003)。
文摘In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.
文摘The existence of a global attractor is established for generalized Navier-Stokes equations incorporating damping term within the periodic domainΩ=[−π,π]^(n).Initially,we show the existence and uniqueness of strong solutions.Subsequently,we verify the continuity of the associated semigroup when max■.Finally,we establish the existence of both H^(α)-global attractor and H^(2α)-global attractor.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11961059,1210502)the University Innovation Project of Gansu Province(Grant No.2023B-062)the Gansu Province Basic Research Innovation Group Project(Grant No.23JRRA684).
文摘The goal of this paper is to investigate the long-time dynamics of solutions to a Kirchhoff type suspension bridge equation with nonlinear damping and memory term.For this problem we establish the well-posedness and existence of uniform attractor under some suitable assumptions on the nonlinear term g(u),the nonlinear damping f(u_(t))and the external force h(x,t).Specifically,the asymptotic compactness of the semigroup is verified by the energy reconstruction method.
基金supported by the National Natural Science Foundation of China(12401482)the second author was supported by the National Natural Science Foundation of China(12371371,12261160361,11971366)supported by the Open Research Fund of Hubei Key Laboratory of Computational Science,Wuhan University.
文摘A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue problem,the method is spectral-correct and spurious-free.Stability and error estimates are obtained,including the interpolation error estimates and the error estimates between the finite element solution and the exact solution.The method is suitable for singular solution as well as smooth solution,and consequently,the method is valid for nonconvex domains which may have a number of reentrant corners.Of course,the method is suitable for arbitrary quadrilaterals(under the usual shape-regular condition).
基金supported by the Guangdong Basic and Applied Basic Research Foundation(2022A1515012138)the NSFC(12271436,12371119)supported by the Natural Science Basic Research Program of Shaanxi(2022JC-04).
文摘We investigate the constrained fractional Choquard equation■where m>0,N>2s with s∈(0,1)being the order of the fractional Laplacian operator and I_(α)forα∈(0,N)denotes the Riesz potential.The parameterμ∈ℝappears as a Lagrange multiplier.By imposing general mass-supercritical conditions on F,we confirm the existence of normalized solutions that characterize the global minimizer on the Pohozaev manifold.Our proof does not depend on the assumption that all weak solutions satisfy the Pohozaev identity,a challenge that remains unsolved for this doubly nonlocal equation.
基金The Natural Science Foundation of Xinjiang Uygur Autonomous Region of China“RBF-Hermite difference scheme for the time-fractional kdv-Burgers equation”(2024D01C43)。
文摘In this paper,we present a finite volume trigonometric weighted essentially non-oscillatory(TWENO)scheme to solve nonlinear degenerate parabolic equations that may exhibit non-smooth solutions.The present method is developed using the trigonometric scheme,which is based on zero,first,and second moments,and the direct discontinuous Galerkin(DDG)flux is used to discretize the diffusion term.Moreover,the DDG method directly applies the weak form of the parabolic equation to each computational cell,which can better capture the characteristics of the solution,especially the discontinuous solution.Meanwhile,the third-order TVD-Runge-Kutta method is applied for temporal discretization.Finally,the effectiveness and stability of the method constructed in this paper are evaluated through numerical tests.
基金Supported by the Korea Health Technology R&D Project through the Korea Health Industry Development Institute(KHIDI),funded by the Ministry of Health&Welfare,Republic of Korea(No.HR20C0026)the National Research Foundation of Korea(NRF)(No.RS-2023-00247504)the Patient-Centered Clinical Research Coordinating Center,funded by the Ministry of Health&Welfare,Republic of Korea(No.HC19C0276).
文摘AIM:To build a functional generalized estimating equation(GEE)model to detect glaucomatous visual field progression and compare the performance of the proposed method with that of commonly employed algorithms.METHODS:Totally 716 eyes of 716 patients with primary open angle glaucoma(POAG)with at least 5 reliable 24-2 test results and 2y of follow-up were selected.The functional GEE model was used to detect perimetric progression in the training dataset(501 eyes).In the testing dataset(215 eyes),progression was evaluated the functional GEE model,mean deviation(MD)and visual field index(VFI)rates of change,Advanced Glaucoma Intervention Study(AGIS)and Collaborative Initial Glaucoma Treatment Study(CIGTS)scores,and pointwise linear regression(PLR).RESULTS:The proposed method showed the highest proportion of eyes detected as progression(54.4%),followed by the VFI rate(34.4%),PLR(23.3%),and MD rate(21.4%).The CIGTS and AGIS scores had a lower proportion of eyes detected as progression(7.9%and 5.1%,respectively).The time to detection of progression was significantly shorter for the proposed method than that of other algorithms(adjusted P≤0.019).The VFI rate displayed moderate pairwise agreement with the proposed method(k=0.47).CONCLUSION:The functional GEE model shows the highest proportion of eyes detected as perimetric progression and the shortest time to detect perimetric progression in patients with POAG.
基金Supported by the National Key Research and Development Program of China(No.2023YFC3008200)the Independent Research Project of Southern Marine Science and Engineering Guangdong Laboratory(Zhuhai)(No.SML2022SP505)。
文摘Physics-informed neural networks(PINNs),as a novel artificial intelligence method for solving partial differential equations,are applicable to solve both forward and inverse problems.This study evaluates the performance of PINNs in solving the temperature diffusion equation of the seawater across six scenarios,including forward and inverse problems under three different boundary conditions.Results demonstrate that PINNs achieved consistently higher accuracy with the Dirichlet and Neumann boundary conditions compared to the Robin boundary condition for both forward and inverse problems.Inaccurate weighting of terms in the loss function can reduce model accuracy.Additionally,the sensitivity of model performance to the positioning of sampling points varied between different boundary conditions.In particular,the model under the Dirichlet boundary condition exhibited superior robustness to variations in point positions during the solutions of inverse problems.In contrast,for the Neumann and Robin boundary conditions,accuracy declines when points were sampled from identical positions or at the same time.Subsequently,the Argo observations were used to reconstruct the vertical diffusion of seawater temperature in the north-central Pacific for the applicability of PINNs in the real ocean.The PINNs successfully captured the vertical diffusion characteristics of seawater temperature,reflected the seasonal changes of vertical temperature under different topographic conditions,and revealed the influence of topography on the temperature diffusion coefficient.The PINNs were proved effective in solving the temperature diffusion equation of seawater with limited data,providing a promising technique for simulating or predicting ocean phenomena using sparse observations.
基金Under the auspices of the National Natural Science Foundation of China(No.42371222,41971167)Fundamental Scientific Research Funds of Central China Normal University(No.CCNU24ZZ120)。
文摘Owing to intensified globalization and informatization,the structures of the urban scale hierarchy and urban networks between cities have become increasingly intertwined,resulting in different spatial effects.Therefore,this paper analyzes the spatial interaction between urban scale hierarchy and urban networks in China from 2019 to 2023,drawing on Baidu migration data and employing a spatial simultaneous equation model.The results reveal a significant positive spatial correlation between cities with higher hierarchy and those with greater network centrality.Within a static framework,we identify a positive interaction between urban scale hierarchy and urban network centrality,while their spatial cross-effects manifest as negative neighborhood interactions based on geographical distance and positive cross-scale interactions shaped by network connections.Within a dynamic framework,changes in urban scale hierarchy and urban networks are mutually reinforcing,thereby widening disparities within the urban hierarchy.Furthermore,an increase in a city’s network centrality had a dampening effect on the population growth of neighboring cities and network-connected cities.This study enhances understanding of the spatial organisation of urban systems and offers insights for coordinated regional development.
基金Supported by National Natural Science Foundation of China(12101482)Postdoctoral Science Foundation of China(2022M722604)+2 种基金General Project of Science and Technology of Shaanxi Province(2023-YBSF-372)The Natural Science Foundation of Shaan Xi Province(2023-JCQN-0016)Shannxi Mathmatical Basic Science Research Project(23JSQ042)。
文摘In order to better describe the phenomenon of biological invasion,this paper introduces a free boundary model of biological invasion.Firstly,the right free boundary is added to the equation with logistic terms.Secondly,the existence and uniqueness of local solutions are proved by the Sobolev embedding theorem and the comparison principle.Finally,according to the relevant research data and contents of red fire ants,the diffusion area and nest number of red fire ants were simulated without external disturbance.This paper mainly simulates the early diffusion process of red fire ants.In the early diffusion stage,red fire ants grow slowly and then spread over a large area after reaching a certain number.
文摘Deep neural networks(DNNs)are effective in solving both forward and inverse problems for nonlinear partial differential equations(PDEs).However,conventional DNNs are not effective in handling problems such as delay differential equations(DDEs)and delay integrodifferential equations(DIDEs)with constant delays,primarily due to their low regularity at delayinduced breaking points.In this paper,a DNN method that combines multi-task learning(MTL)which is proposed to solve both the forward and inverse problems of DIDEs.The core idea of this approach is to divide the original equation into multiple tasks based on the delay,using auxiliary outputs to represent the integral terms,followed by the use of MTL to seamlessly incorporate the properties at the breaking points into the loss function.Furthermore,given the increased training dificulty associated with multiple tasks and outputs,we employ a sequential training scheme to reduce training complexity and provide reference solutions for subsequent tasks.This approach significantly enhances the approximation accuracy of solving DIDEs with DNNs,as demonstrated by comparisons with traditional DNN methods.We validate the effectiveness of this method through several numerical experiments,test various parameter sharing structures in MTL and compare the testing results of these structures.Finally,this method is implemented to solve the inverse problem of nonlinear DIDE and the results show that the unknown parameters of DIDE can be discovered with sparse or noisy data.
文摘In order to solve the problem of the variable coefficient ordinary differen-tial equation on the bounded domain,the Lagrange interpolation method is used to approximate the exact solution of the equation,and the error between the numerical solution and the exact solution is obtained,and then compared with the error formed by the difference method,it is concluded that the Lagrange interpolation method is more effective in solving the variable coefficient ordinary differential equation.
基金funded by the Research program FMUW-2021-0002 of the IPGG RAS.
文摘An equation of state(EOS)was obtained that accurately describes the thermodynamics of the system H_(2)O–CO_(2) at temperatures of 50–350°C and pressures of 0.2–3.5 kbar.The equation is based on experimental data on the compositions of the coexisting liquid and gas phases and the Van Laar model,within which the values of the Van Laar parameters A12 and A21 were found for each experimental P-T point.For the resulting sets A12(P,T),A21(P,T),approximation formulas describing the dependences of these quantities on temperature and pressure were found and the parameters contained in the formulas were fitted.This two-stage approach made it possible to obtain an adequate thermodynamic description of the system,which allows,in addition to determining the phase state of the system(homogeneous or heterogeneous),to calculate the excess free energy of mixing of H_(2)O and CO_(2),the activities of H_(2)O and CO_(2),and other thermodynamic characteristics of the system.The possibility of such calculations creates the basis for using the obtained EOS in thermodynamic models of more complicated fluid systems in P-T conditions of the middle and upper crust.These fluids play an important role in many geological processes including the transport of ore matter and forming hydrothermal ore deposits,in particular,the most of the world’s gold deposits.The knowledge of thermodynamics of these fluids is important in the technology of drilling oil and gas wells.In particular,this concerns the prevention of precipitation of solid salts in the well.
基金Supported by National Science Foundation of China(11971027,12171497)。
文摘This paper deals with quasilinear elliptic equations of singular growth like-Δu-uΔ(u^(2))=a(x)u^(-1).We establish the existence of positive solutions for general a(x)∈L^(p)(Ω),p>2,whereΩis a bounded domain inℝ^(N)with N≥1.
文摘Reference crop evapotranspiration (ETo) is essential for irrigation, water resources management and environmental assessment. The indirect estimation of ETo is based a) on energy budget approach using meteorological data and b) pan evaporation measurements (Epan) multiplied by pan coefficients (kp) adapted to the surrounding environmental conditions. Significant interest is shown for the kp equations, which have to be tested before their use. The purpose of this study is to evaluate six different kp equations, such as those of Cuenca, Allen and Puitt, Snyder, Pereira et al., Orang, Raghuwanshi and Wallender for the summer growing season (April to October) of Thessaloniki plain in Greece, which is characterized by a semi-arid Mediterranean environment. The evaluation of the kp equations is performed by two years Epan measurements, using as reference the daily ETo values estimated by the ASCE-standardized Penman-Monteith equation (ASCE-PM) in hourly time step. The results of this study showed that Cuenca’s equation provided more accurate daily estimations. Additional analysis is performed in other methods such as those of FAO-56 and Hargreaves based on the calculation time step (hourly or daily) and their correspondence to the ASCE-PM.
基金Supported by the National Natural Science Foundation of China(12071162)the Natural Science Foundation of Fujian Province(2021J01302)the Fundamental Research Funds for the Central Universities(ZQN-802).
文摘In this paper,we focus on peaked traveling wave solutions of the modified highly nonlinear Novikov equation by dynamical systems approach.We obtain a traveling wave system which is a singular planar dynamical system with three singular straight lines,and derive all possible phase portraits under corresponding parameter conditions.Then we show the existence and dynamics of two types of peaked traveling wave solutions including peakons and periodic cusp wave solutions.The exact explicit expressions of two peakons are given.Besides,we also derive smooth solitary wave solutions,periodic wave solutions,compacton solutions,and kink-like(antikink-like)solutions.Numerical simulations are further performed to verify the correctness of the results.Most importantly,peakons and periodic cusp wave solutions are newly found for the equation,which extends the previous results.
基金Supported by the National Natural Science Foundation of China(11671403,11671236,12101192)Henan Provincial General Natural Science Foundation Project(232300420113)。
文摘In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with prescribed 2-norm has some normalized solutions by introducing variational methods.
基金Supported by the National Natural Science Foundation of China(12071162)the Natural Science Foundation of Fujian Province(2021J01302)the Fundamental Research Funds for the Central Universities(ZQN-802)。
文摘This paper deals with the monotonicity of limit wave speed c0(h)to a perturbed g KdV equation.We show the decrease of c0(h)by combining the analytic method and the numerical technique.Our results solve a special case of the open question presented by Yan et al.,and the method potentially provides a way to study the monotonicity of c0(h)for general m∈N^(+).
