Traveling waves in reaction–diffusion–convection equations with combustion nonlinearity

Abstract

This paper concerns the existence and properties of traveling wave solutions to reaction–diffusion–convection equations on the real line. We consider a general diffusion term involving the $p$-Laplacian and combustion-type reaction term. We extend and generalize results established for $p=2$ to the case of singular and degenerate diffusion. Our approach allows for non-Lipschitz reaction as well. We also discuss the shape of the traveling wave profile near equilibria, assuming power-type behavior of the reaction and diffusion terms.