Traveling waves for highly degenerate and singular reaction-diffusion-advection equations with discontinuous coefficients

TL;DR

This paper establishes conditions for the existence or non-existence of traveling wave solutions in complex reaction-diffusion-advection equations with degeneracies and discontinuities, and characterizes admissible wave speeds.

Contribution

It provides new criteria and bounds for traveling wave solutions in highly degenerate or singular equations with discontinuous coefficients.

Findings

Conditions for existence and non-existence of traveling waves.

Characterization of admissible wave speeds.

Estimation of minimum wave speed bounds.

Abstract

Sufficient conditions for either existence or non-existence of traveling wave solutions for a general quasi-linear reaction-diffusion-convection equation, possibly highly degenerate or singular, with discontinuous coefficients are furnished. Under an additional hypothesis on the convection term, the set of admissible wave speeds is characterized in terms of the minimum wave speed, which is estimated through a double-sided bound.