On the stability of periodic solutions of multi-dimensional models

Abstract

We consider a class of multi-dimensional models and prove the existence of non-trivial steady periodic waves. One of the main results is concerned with the spectral instability of a stationary periodic wave, proved by means of Floquet's theory and the introduction of the Evans function for a suitable related eigenvalue problem. A description of the zero set of the Evans function around the origin allows us to establish a link between the spectral stability analysis and a first-order system of conservation laws derived from the original model through homogenisation.