Blowup of the Solutions for a Reaction-Advection-Diffusion Equation with Free Boundaries

Abstract

We investigate a blowup problem of a reaction-advection-diffusion equation with double free boundaries and aim to use the dynamics of such a problem to describe the heat transfer and temperature change of a chemical reaction in advective environment with the free boundary representing the spreading front of the heat. We study the influence of the advection on the blowup properties of the solutions and conclude that large advection is not favorable for blowup. Moreover, we give the decay estimates of solutions and the two free boundaries converge to a finite limit for small initial data.