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Using the advection-diffusion equation, we analytically study contaminant transport in a sharply contrasting medium with a diffusion barrier due to localization of a contaminant source in a low-permeability medium. Anomalous diffusion…
This paper is concerned with the interaction between a planar traveling front and a compact obstacle for monotone bistable reaction-diffusion systems in exterior domains. By constructing appropriate sub- and supersolutions, we first…
Second initial boundary problem in narrow domains of width $\epsilon\ll 1$ for linear second order differential equations with nonlinear boundary conditions is considered in this paper. Using probabilistic methods we show that the solution…
This paper is concerned with some nonlinear propagation phenomena for reaction-advection-diffusion equations with Kolmogrov-Petrovsky-Piskunov (KPP) type nonlinearities in general periodic domains or in infinite cylinders with oscillating…
In this paper we consider a model for the diffusion of a population in a strip-shaped field, where the growth of the species is governed by a Fisher-KPP equation and which is bounded on one side by a road where the species can have a…
This paper is concerned with a model for the dynamics of a single species in a one-dimensional heterogeneous environment. The environment consists of two kinds of patches, which are periodically alternately arranged along the spatial axis.…
We consider a monostable time-delayed reaction-diffusion equation arising from population dynamics models. We let a small parameter tend to zero and investigate the behavior of the solutions. We construct accurate lower barriers --- by…
This short paper concerns a diffusive logistic equation with the heterogeneous environment and a free boundary, which is formulated to study the spread of an invasive species, where the free boundary represents the expanding front. A…
Spatial heterogeneity and habitat characteristic are shown to determine the asymptotic profile of the solution to a reaction-diffusion model with free boundary, which describes the moving front of the invasive species. A threshold value…
In this paper, we study the dynamics of a two-species competition model with two different free boundaries in heterogeneous time-periodic environment, where the two species adopt a combination of random movement and advection upward or…
Reaction-advection-diffusion equations, in periodic settings and with general type nonlinearities, admit a threshold known as the minimal speed of propagation. The minimal speed does not have an accessible formula when the nonlinearity is…
We study a class of free boundary problems of ecological models with nonlocal and local diffusions, which are natural extensions of free boundary problems of reaction diffusion systems in there local diffusions are used to describe the…
In this paper we consider the diffusive competition model with free boundary in the heterogeneous time-periodic environment, in which the variable intrinsic growth rates of invasive and native species may change signs and be "very negative"…
In this paper we study the following one-dimensional reaction-diffusion problem $$ u_t+(-\Delta)^s u=f(x-c t, u) \;\:\textrm{ in } \mathbb{R}\times (0,+\infty), $$ where $s>\frac{1}{2}$, $c \in \mathbb{R}$ is a prescribed velocity, and $f$…
We consider a stochastically perturbed reaction diffusion equation in a bounded interval, with boundary conditions imposing the two stable phases at the endpoints. We investigate the asymptotic behavior of the front separating the two…
A general reaction-diffusion equation with spatiotemporal delay and homogeneous Dirichlet boundary condition is considered. The existence and stability of positive steady state solutions are proved via studying an equivalent…
We investigate the large time behavior of solutions of reaction-diffusion equations with general reaction terms in periodic media. We first derive some conditions which guarantee that solutions with compactly supported initial data invade…
In this paper we derive quantitative conditions under which a compactly supported drift term depending on the direction of propagation blocks a traveling wave solution or lets it pass almost unchanged. We give explicit conditions on the…
In this paper, we study the existence and stability of travelling wave solutions of a kinetic reaction-transport equation. The model describes particles moving according to a velocity-jump process, and proliferating thanks to a reaction…
We study existence and uniqueness of travelling fronts, and asymptotic speed of propagation for a non local reaction diffusion equation with spatial and genetic trait structure.