Stability of traveling waves for autocatalytic reaction systems with strong decay

Abstract

This paper is concerned with the spatial decay and stability of travelling wave solutions for a reaction diffusion system $u_{t}=d u_{xx}-uv$, $v_{t}=v_{xx}+uv-Kv^{q}$ with $q>1$. By applying Centre Manifold Theorem and detailed asymptotic analysis, we get the precise spatial decaying rate of the travelling waves with noncritical speeds. Further by applying spectral analysis, Evans function method and some numerical simulation, we proved the spectral stability and the linear exponential stability of the waves with noncritical speeds in some weighted spaces.