Related papers: Bistable reaction equations with doubly nonlinear …
In this paper, we study the large time behaviour of solutions of multistable reaction-diffusion equations in $\mathbb{R}^N$, with a spatially periodic heterogeneity. By multistable, we mean that the problem admits a finite -- but…
We prove existence and uniqueness of travelling waves for a reaction-diffusion system coupling a classical reaction-diffusion equation in a strip with a diffusion equation on a line. To do this we use a continuation method which leads to…
In this paper the travelling wave solutions in the adiabatic model with two-step chain branching reaction mechanism are investigated both numerically and analytically in the limit of equal diffusivity of reactant, radicals and heat. The…
We consider reaction-diffusion systems on the infinite line that exhibit a family of spectrally stable spatially periodic wave trains $u_0(kx-\om t;k)$ that are parameterized by the wave number $k$. We prove stable diffusive mixing of the…
We investigate the asymptotic behavior of the a large class of reversible chemical reaction-diffusion equations with the same diffusion. In particular we prove the optimal rate in two cases : when there is no diffusion and in the classical…
We study a non-linear convective-diffusive equation, local in space and time, which has its background in the dynamics of the thickness of a wetting film. The presence of a non-linear diffusion predicts the existence of fronts as well as…
Convective counterparts of variants of the nonlinear Fisher equation which describes reaction diffusion systems in population dynamics are studied with the help of an analytic prescription and shown to lead to interesting consequences for…
A nonlinear PDE featuring flux limitation effects together with those of the porous media equation (nonlinear Fokker-Planck) is presented in this paper. We analyze the balance of such diverse effects through the study of the existence and…
We classify traveling waves and stationary solutions of a reaction-diffusion equation arising in population dynamics with Allee-type effects. The reaction term is given by a quadratic polynomial with a discontinuity at zero, which captures…
We prove the existence and uniqueness of a traveling front and of its speed for the homogeneous heat equation in the half-plane with a Neumann boundary reaction term of non-balanced bistable type or of combustion type. We also establish the…
This paper is concerned with the traveling waves of delayed reaction-diffusion systems where the reaction function possesses the mixed quasimonotonicity property. By the so-called monotone iteration scheme and Schauder's fixed point…
We study analytically and numerically a bistable reaction-diffusion equation on an arbitrary finite network. We prove that stable fixed points (multi-fronts) exist for any configuration as long as the diffusion is small. We also study fold…
In this paper we will establish nonlinear a priori lower and upper bounds for the solutions to a large class of equations which arise from the study of traveling wave solutions of reaction-diffusion equations, and we will apply our…
Based on a recent work on traveling waves in spatially nonlocal reaction-diffusion equations, we investigate the existence of traveling fronts in reaction-diffusion equations with a memory term. We will explain how such memory terms can…
Nonlinear waves are studied in a mixture of liquid and gas bubbles. Influence of viscosity and heat transfer is taken into consideration on propagation of the pressure waves. Nonlinear evolution equations of the second and the third order…
We study the asymptotics of Allen-Cahn-type bistable reaction-diffusion equations which are additively perturbed by a stochastic forcing (time white noise). The conclusion is that the long time, large space behavior of the solutions is…
We study the traveling wave solutions to a reaction diffusion system modeling the public goods game with altruistic behaviors. The existence of the waves is derived through monotone iteration of a pair of classical upper- and lower…
In this article we are concerned with the existence and orbital stability of traveling wave solutions of a general class of nonlocal wave equations: $ u_{tt}-Lu_{xx}=B(\pm |u|^{p-1}u)_{xx}$, $ p>1$. The main characteristic of this class of…
In this paper, we study the existence of traveling wave solutions and the spreading speed for the solutions of an age-structured epidemic model with nonlocal diffusion. Our proofs make use of the comparison principles both to construct…
We address the question: Why may reaction-diffusion equations with hysteretic nonlinearities become ill-posed and how to amend this? To do so, we discretize the spatial variable and obtain a lattice dynamical system with a hysteretic…