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

TL;DR

This paper investigates traveling wave solutions in reaction-diffusion-convection equations with combustion nonlinearities, extending existing results to include singular and degenerate diffusion and non-Lipschitz reactions.

Contribution

It generalizes previous work by considering p-Laplacian diffusion and non-Lipschitz reactions, analyzing wave profiles near equilibria.

Findings

Existence of traveling waves for singular and degenerate diffusion cases.

Characterization of wave profile shapes near equilibria.

Extension of results from classical to generalized diffusion and reaction terms.

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 the 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.