Heteroclinic traveling fronts for a generalized Fisher-Burgers equation with saturating diffusion

TL;DR

This paper investigates the existence and properties of monotone heteroclinic traveling waves in a generalized Fisher-Burgers equation with saturating, density-dependent diffusion, providing estimates for critical wave speeds and analyzing parameter effects through numerical simulations.

Contribution

It introduces new analysis of heteroclinic traveling waves in a Fisher-Burgers model with saturating diffusion, including critical speed estimates and parameter dependence.

Findings

Critical speed estimates for different reaction term shapes

Dependence of wave speed on small parameters affecting diffusion

Numerical simulations supporting theoretical results

Abstract

We study the existence of monotone heteroclinic traveling waves for a general Fisher-Burgers equation with nonlinear and possibly density-dependent diffusion. Such a model arises, for instance, in physical phenomena where a saturation effect appears for large values of the gradient. We give an estimate for the critical speed (namely, the first speed for which a monotone heteroclinic traveling wave exists) for some different shapes of the reaction term, and we analyze its dependence on a small real parameter when this brakes the diffusion, complementing our study with some numerical simulations.