Curved fronts in a shear flow: case of combustion nonlinearities

TL;DR

This paper establishes the existence and uniqueness of curved traveling fronts in a reaction-advection-diffusion model with combustion nonlinearities, analyzing flame shapes under shear flow and deriving their propagation speed.

Contribution

It provides the first rigorous proof of curved front solutions and their speeds in a shear flow with combustion nonlinearities, extending previous planar wave results.

Findings

Existence and uniqueness of curved traveling fronts proven.

Derived formula for front propagation speed in shear flow.

Application to flame shapes in Bunsen burners.

Abstract

We prove the existence and uniqueness, up to a shift in time, of curved traveling fronts for a reaction-advection-diffusion equation with a combustion-type nonlinearity. The advection is through a shear flow $q$. This analyzes, for instance, the shape of flames produced by a Bunsen burner in the presence of advection. We also give a formula for the speed of propagation of these conical fronts in terms of the well-known speed of planar pulsating traveling waves.