相关论文: On monostable cooperative system with nonlocal dif…
Spiral waves are a ubiquitous feature of the nonequilibrium dynamics of a great variety of excitable systems. In the limit of a large separation in timescale between fast excitation and slow recovery, one can reduce the spiral problem to…
This paper concerns the spreading speed and asymptotical behaviors, which was left as an open problem in \cite{LLW22}, of a Fisher-KPP nonlocal diffusion model with a free boundary. Using a new lower solution, we get the exact finite…
We study the spreading speed of a diffusive epidemic model proposed by Li et al. \cite{LL}, where the Stefan boundary condition is imposed at the right boundary, and the left boundary is subject to the homogeneous Dirichlet and Neumann…
We study a reaction-diffusion equation with a nonlocal reaction term that models a population with variable motility. We establish a global supremum bound for solutions of the equation. We investigate the asymptotic (long-time and…
In this paper we study asymptotic behavior of solutions for a free boundary problem modeling the growth of tumors containing two species of cells: proliferating cells and quiescent cells. This tumor model was proposed by Pettet et al in…
This is the third part of our series of work devoted to the dynamics of an epidemic model with nonlocal diffusions and free boundary. This part is concerned with the rate of accelerated spreading for three types of kernel functions when…
We study the Cauchy problem for nonlocal reaction diffusion equations with bistable nonlinearity in 1D spatial domain and investigate the asymptotic behaviors of solutions with a one-parameter family of monotonically increasing and…
In this series of papers, we investigate the spreading and vanishing dynamics of time almost periodic diffusive KPP equations with free boundaries. Such equations are used to characterize the spreading of a new species in time almost…
In a previous paper(2021), the author studied the asymptotic behavior of coexistence steady-states to the Shigesada-Kawasaki-Teramoto model as both cross-diffusion coefficients tend to infinity at the same rate. As a result, he proved that…
In this article we investigate two free boundary problems for a Lotka-Volterra competition system in a higher space dimension with sign-changing coefficients. One may be viewed as describing how two competing species invade if they occupy…
We study the asymptotic diffusion processes with (generally nonlocal) open boundaries in one dimension which are exactly solvable by means of the recently developed recursion formula. We investigate the stationary states, which cannot be…
In this volume a theory for models of transport in the presence of a free boundary is developed. Macroscopic laws of transport are described by PDEs. When the system is open, there are several mechanisms to couple the system with the…
In this paper we investigate two free boundary problems for a Lotka-Volterra type competition model in one space dimension. The main objective is to understand the asymptotic behavior of the two competing species spreading via a free…
This work investigates the diffusion of cooperative behavior over time in a decentralized cognitive radio network with selfish spectrum-sensing users. The users can individually choose whether or not to participate in cooperative spectrum…
This work examines the limits of the principal spectrum point, $\lambda_p$, of a nonlocal dispersal cooperative system with respect to the dispersal rates. In particular, we provide precise information on the sign of $\lambda_p$ as one of…
The current series of research papers is to investigate the asymptotic dynamics in logistic type chemotaxis models in one space dimension with a free boundary or unbounded boundary. Such a model with a free boundary describes the spreading…
We investigate two-phase flow in porous media and derive a two-scale model, which incorporates pore-scale phase distribution and surface tension into the effective behavior at the larger Darcy scale. The free-boundary problem at the pore…
The current series of research papers is to investigate the asymptotic dynamics in logistic type chemotaxis models in one space dimension with a free boundary or an unbounded boundary. Such a model with a free boundary describes the…
We discuss the analysis and stability of a family of cross-diffusion boundary value problems with nonlinear diffusion and drift terms. We assume that these systems are close, in a suitable sense, to a set of decoupled and linear problems.…
We study the long time behavior of solutions of the Cauchy problem for nonlinear reaction-diffusion equations in one space dimension with the nonlinearity of bistable, ignition or monostable type. We prove a one-to-one relation between the…