In this paper,we derive rigorously a non-local cross-diffusion system from an interacting stochastic many-particle system in the whole space.The convergence is proved in the sense of probability by introducing an inte...In this paper,we derive rigorously a non-local cross-diffusion system from an interacting stochastic many-particle system in the whole space.The convergence is proved in the sense of probability by introducing an intermediate particle system with a mollified interaction potential,where the mollification is of algebraic scaling.The main idea of the proof is to study the time evolution of a stopped process and obtain a Gronwall type estimate by using Taylor's expansion around the limiting stochastic process.展开更多
This paper is concerned with the global existence of solutions for a class of quasilinear cross-diffusion system describing two species competition under self and cross population pressure. By establishing and using m...This paper is concerned with the global existence of solutions for a class of quasilinear cross-diffusion system describing two species competition under self and cross population pressure. By establishing and using more detailed interpolation results between several different Banach spaces, the global existence of solutions are proved when the self and cross diffusion rates for the first species are positive and there is no self or cross-diffusion for the second species.展开更多
In this paper, we investigate the positive solutions of strongly coupled nonlinear parabolic systems with nonlinear boundary conditions： {ut-a（u, v）△u=g（u, v）, vt-b（u, v）△v=h（u, v）, δu/δη=d（u, v）, δu...In this paper, we investigate the positive solutions of strongly coupled nonlinear parabolic systems with nonlinear boundary conditions： {ut-a（u, v）△u=g（u, v）, vt-b（u, v）△v=h（u, v）, δu/δη=d（u, v）, δu/δη=f（u, v）.Under appropriate hypotheses on the functions a, b, g, h, d and f, we obtain that the solutions may exist globally or blow up in finite time by utilizing upper and lower solution techniques.展开更多
This paper is concerned with a ratio-dependent predator-prey system with diffusion and cross- diffusion in a bounded domain with no flux boundary condition. We show that under certain hypotheses, the cross-diffusion c...This paper is concerned with a ratio-dependent predator-prey system with diffusion and cross- diffusion in a bounded domain with no flux boundary condition. We show that under certain hypotheses, the cross-diffusion can create non-constant positive steady states even though the corresponding model without cross-diffusion fails.展开更多
This paper investigates a strongly coupled reaction-diffusion model with Holling-II reaction function in a bounded domain with homogeneous Neumann boundary condition. The sufficient condition for the existence and non...This paper investigates a strongly coupled reaction-diffusion model with Holling-II reaction function in a bounded domain with homogeneous Neumann boundary condition. The sufficient condition for the existence and non-existence of the non-constant positive solutions are obtained. Moreover, we prove that the nonlinear diffusion terms can create non-constant positive equilibrium solutions when the corresponding model without nonlinear diffusion term fails.展开更多
This paper is concerned with the existence and stability of steady state solutions for the SKT biological competition model with cross-diffusion.By applying the detailed spectral analysis and in virtue of the bifurcat...This paper is concerned with the existence and stability of steady state solutions for the SKT biological competition model with cross-diffusion.By applying the detailed spectral analysis and in virtue of the bifurcating direction to the limiting system as the cross diffusion rate tends to infinity,it is proved the stability/instability of the nontrivial positive steady states with some special bifurcating structure.Further,the existence and stability/instability of the corresponding nontrivial positive steady states for the original cross-diffusion system are proved by applying perturbation argument.展开更多
A strongly coupled elliptic system under the homogeneous Dirichlet boundary condition denoting the steady-state system of the Lotka-Volterra two-species competitive system with cross-diffusion effects is considered. B...A strongly coupled elliptic system under the homogeneous Dirichlet boundary condition denoting the steady-state system of the Lotka-Volterra two-species competitive system with cross-diffusion effects is considered. By using the implicit function theorem and the Lyapunov- Schmidt reduction method, the existence of the positive solutions bifurcating from the trivial solution is obtained. Furthermore, the stability of the bifurcating positive solutions is also investigated by analyzing the associated characteristic equation.展开更多
This paper considers a kind of strongly coupled cross diffusion parabolic system, which can be used as the multi-dimensional Lyurnkis energy transport model in semiconductor science. The global existence and large tim...This paper considers a kind of strongly coupled cross diffusion parabolic system, which can be used as the multi-dimensional Lyurnkis energy transport model in semiconductor science. The global existence and large time behavior are obtained for smooth solution to the initial boundary value problem. When the initial data are a small perturbation of an isothermal stationary solution, the smooth solution of the problem under the insulating boundary condition, converges to that stationary solution exponentially fast as time goes to infinity.展开更多
In the present work we study the global solvability of the Kolmogorov-Fisher type biological population task with double nonlinear diffusion and qualitative properties of the solution of the task based on the self-sim...In the present work we study the global solvability of the Kolmogorov-Fisher type biological population task with double nonlinear diffusion and qualitative properties of the solution of the task based on the self-similar analysis. In additional, in this paper we consider the model of two competing population with dual nonlinear cross-diffusion.展开更多
基金funding from the European Research Council (ERC)under the European Union's Horizon 2020 research and innovation programme,ERC Advanced Grant No.101018153support from the Austrian Science Fund (FWF) (Grants P33010,F65)supported by the NSFC (Grant No.12101305).
文摘In this paper,we derive rigorously a non-local cross-diffusion system from an interacting stochastic many-particle system in the whole space.The convergence is proved in the sense of probability by introducing an intermediate particle system with a mollified interaction potential,where the mollification is of algebraic scaling.The main idea of the proof is to study the time evolution of a stopped process and obtain a Gronwall type estimate by using Taylor's expansion around the limiting stochastic process.
文摘This paper is concerned with the global existence of solutions for a class of quasilinear cross-diffusion system describing two species competition under self and cross population pressure. By establishing and using more detailed interpolation results between several different Banach spaces, the global existence of solutions are proved when the self and cross diffusion rates for the first species are positive and there is no self or cross-diffusion for the second species.
文摘In this paper, we investigate the positive solutions of strongly coupled nonlinear parabolic systems with nonlinear boundary conditions： {ut-a（u, v）△u=g（u, v）, vt-b（u, v）△v=h（u, v）, δu/δη=d（u, v）, δu/δη=f（u, v）.Under appropriate hypotheses on the functions a, b, g, h, d and f, we obtain that the solutions may exist globally or blow up in finite time by utilizing upper and lower solution techniques.
基金Supported in part by the National Natural Science Foundation of China under Grant No.11601542 and 11626238
文摘This paper is concerned with a ratio-dependent predator-prey system with diffusion and cross- diffusion in a bounded domain with no flux boundary condition. We show that under certain hypotheses, the cross-diffusion can create non-constant positive steady states even though the corresponding model without cross-diffusion fails.
基金Supported by the National Natural Science Foundation of China (11001160)the Scientific Research Plan Projects of Shaanxi Education Department (09JK480)the President Fund of Xi’an Technological University(XAGDXJJ0830)
文摘This paper investigates a strongly coupled reaction-diffusion model with Holling-II reaction function in a bounded domain with homogeneous Neumann boundary condition. The sufficient condition for the existence and non-existence of the non-constant positive solutions are obtained. Moreover, we prove that the nonlinear diffusion terms can create non-constant positive equilibrium solutions when the corresponding model without nonlinear diffusion term fails.
基金supported by the National Natural Science Foundation of China(No.11871048,No.11501031,No.11471221,No.11501016)Premium Funding Project for Academic Human Resources Development in Beijing Union University(BPHR2019CZ07,BPHR2020EZ01)Beijing Municipal Education Commission(KZ201310028030,KM202011417010)。
文摘This paper is concerned with the existence and stability of steady state solutions for the SKT biological competition model with cross-diffusion.By applying the detailed spectral analysis and in virtue of the bifurcating direction to the limiting system as the cross diffusion rate tends to infinity,it is proved the stability/instability of the nontrivial positive steady states with some special bifurcating structure.Further,the existence and stability/instability of the corresponding nontrivial positive steady states for the original cross-diffusion system are proved by applying perturbation argument.
基金Supported by the National Natural Science Foundation of China (10961017)"Qinglan" Talent Programof Lanzhou Jiaotong University (QL-05-20A)
文摘A strongly coupled elliptic system under the homogeneous Dirichlet boundary condition denoting the steady-state system of the Lotka-Volterra two-species competitive system with cross-diffusion effects is considered. By using the implicit function theorem and the Lyapunov- Schmidt reduction method, the existence of the positive solutions bifurcating from the trivial solution is obtained. Furthermore, the stability of the bifurcating positive solutions is also investigated by analyzing the associated characteristic equation.
基金the National Natural Science Foundation of China (No.10401019)the DFG priority research program ANurnE (DFG Wa 633/9-2)National Natural Science Foundation of China (No. 10431060).
文摘This paper considers a kind of strongly coupled cross diffusion parabolic system, which can be used as the multi-dimensional Lyurnkis energy transport model in semiconductor science. The global existence and large time behavior are obtained for smooth solution to the initial boundary value problem. When the initial data are a small perturbation of an isothermal stationary solution, the smooth solution of the problem under the insulating boundary condition, converges to that stationary solution exponentially fast as time goes to infinity.
文摘In the present work we study the global solvability of the Kolmogorov-Fisher type biological population task with double nonlinear diffusion and qualitative properties of the solution of the task based on the self-similar analysis. In additional, in this paper we consider the model of two competing population with dual nonlinear cross-diffusion.
