相关论文: Transition between linear and exponential propagat…

We consider a class of cooperative reaction-diffusion systems with free boundaries in one space dimension, where the diffusion terms are nonlocal, given by integral operators involving suitable kernel functions, and they are allowed not to…

We investigate in this paper a scalar reaction diffusion equation with a nonlinear reaction term depending on x-ct. Here, c is a prescribed parameter modelling the speed of climate change and we wonder whether a population will survive or…

This paper explores the exponential stability of two nonlinear wave equations coupled through their velocities. The analysis is divided into two main cases. First, we consider a system where one equation is damped, while the other…

Spatio-temporal dynamics of the evolution of population involving growth and diffusion processes can be modeled by class of partial diffusion equations (PDEs) known as reaction-diffusion systems. In this work, we developed a nonlinear…

We introduce a novel numerical method for direct simulation of front propagation in the Fisher-KPP equation with a time-dependent parameter on an infinite domain. The method computes a time-dependent boundary condition that accurately…

We treat a model of population dynamics in a periodic environment presenting a fast diffusion line. This phenomenon is modelled via a "road-field" system, which is a system of coupled reaction-diffusion equations set in domains of different…

We address the propagation into an unstable state of a localised disturbance in a forward-backward diffusion pseudo-parabolic equation. Three asymptotic regimes are distinguished as t tends to infinity, the first being a regime ahead of the…

This paper is devoted to the study of propagation phenomena for a Lotka-Volterra reaction-advection-diffusion competition model in a periodic habitat. We first investigate the global attractivity of a semi-trival steady state for the…

The reaction-diffusion model can generate a wide variety of spatial patterns, which has been widely applied in chemistry, biology, and physics, even used to explain self-regulated pattern formation in the developing animal embryo. In this…

Analysis of the speed of propagation in parabolic operators is frequently carried out considering the minimal speed at which its traveling waves move. This value depends on the solution concept being considered. We analyze an extensive…

We consider a coupled reaction-advection-diffusion system based on the Fisher-KPP and Burgers equations. These equations serve as a one-dimensional version of a model for a reacting fluid in which the arising density differences induce a…

Invasion waves are a fundamental building block of theoretical ecology. In this study we aim to take the first steps to link propagation failure and fast acceleration of traveling waves to critical transitions (or tipping points). The…

A linear growth-diffusion equation is studied in a time-dependent interval whose location and length both vary. We prove conditions on the boundary motion for which the solution can be found in exact form, and derive the explicit expression…

The solution h to the Fisher-KPP equation with a steep enough initial condition develops into a front moving at velocity 2, with logarithmic corrections to its position. In this paper we investigate the value h(c t, t) of the solution ahead…

This is part two of our study on the spreading properties of the Lotka-Volterra competition-diffusion systems with a stable coexistence state. We focus on the case when the initial data are exponential decaying. By establishing a comparison…

We study the large time asymptotics of a solution of the Fisher-KPP reaction-diffusion equation, with an initial condition that is a compact perturbation of a step function. A well-known result of Bramson states that, in the reference frame…

The current paper is devoted to the study of semilinear dispersal evolution equations of the form $$ u_t(t,x)=(\mathcal{A}u)(t,x)+u(t,x)f(t,x,u(t,x)),\quad x\in\mathcal{H}, $$ where $\mathcal{H}=\RR^N$ or $\ZZ^N$, $\mathcal{A}$ is a random…

This paper is devoted to propagation phenomena for a reaction-diffusion-advection equation in a one-dimensional heterogeneous environment, where heterogeneity is reflected by the nonlinearity term -- being KPP type on $(-\infty, -L]$ and…

We establish in this article spreading properties for the solutions of equations of the type $\partial$ t u -- a(x)$\partial$ xx u -- q(x)$\partial$ x u = f (x, u), where a, q, f are only assumed to be uniformly continuous and bounded in x,…

The propagation of light in a scattering medium is described as the motion of a special kind of a Brownian particle on which the fluctuating forces act only perpendicular to its velocity. This enforces strictly and dynamically the…