Stability of Travelling Waves for a Cross-Diffusion Model

Travelling waves in a reaction-diffusion model for electrodeposition

In this paper we consider an analytical and numerical study of a reaction-diffusion system for describing the formation of transition front waves in some electrodeposition (ECD) experiments. Towards this aim, a model accounting for the coupling between morphology and composition of one chemical species adsorbed at the surface of the growing cathode is addressed. Through a phase-space analysis w...

Stability of Travelling Waves

Stability of travelling waves

An overview of various aspects related to the spectral and nonlinear stability of travelling-wave solutions to partial differential equations is given. The point and the essential spectrum of the linearization about a travelling wave are discussed as is the relation between these spectra, Fredholm properties, and the existence of exponential dichotomies (or Green’s functions) for the linear ope...

Generalized travelling waves for reaction-diffusion equations

In this paper, we introduce a generalization of travelling waves for evolution equations. We are especially interested in reaction-diffusion equations and systems in heterogeneous media (with general operators and general geometry). Our goal is threefold. First we give several definitions, for transition waves, fronts, pulses, global mean speed of propagation, etc. Next, we discuss the meaning ...

Travelling Waves for Reaction-diffusion-convection Systems

(1) ut = Auxx + f(u), u ∈ R , x ∈ R, t ∈ [0,∞), where A is a real, positive-definite, N × N matrix and f : R → R is a continuously differentiable nonlinear function. The vector u may represent, for example, the concentrations of chemicals or the population densities of interacting species, the interactions between components of u being modelled by the reaction term f(u) and their diffusion by A...