The role of convection in the limit shape of the critical front profile for Born-Infeld diffusion models

TL;DR

This paper investigates how convection influences the shape of critical front profiles in Born-Infeld diffusion models with monostable reactions, revealing that convection can either sharpen or regularize the profile.

Contribution

It provides new insights into the effect of convection on the limit shape of critical fronts in Born-Infeld diffusion models, including estimates of critical speed and analysis of profile regularization.

Findings

Convection can sharpen the front profile.

Convection can also regularize the front profile.

Numerical simulations support theoretical results.

Abstract

In this paper, we deal with models with Born-Infeld type diffusion and monostable reaction, investigating the effect of the introduction of a convection term on the limit shape of the critical front profile for vanishing diffusion. We first provide an estimate of the critical speed and then, through a careful analysis of an equivalent first-order problem, we show that different convection terms may lead either to a complete sharpening of the limit profile or to its complete regularization, presenting some related numerical simulations.