Stability of travelling waves in a model for conical flames in two space dimensions

Abstract

This paper deals with the question of the stability of conical-shaped solutions of a class of reaction-diffusion equations in $\R^2$. One first proves the existence of travelling waves solutions with conical-shaped level sets, generalizing earlier results by Bonnet, Hamel and Monneau. One then gives a characterization of the global attractor of these semilinear parabolic equations under some conical asymptotic conditions. Lastly, the global stability of the travelling waves solutions is proved