Blowup of the Solutions for a Reaction-Advection-Diffusion Equation with Free Boundaries (Journal of Partial Differential Equations, 2023)
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 todescribe the heat transfer and temperature change of a chemical reaction in advectiveenvironment with the free boundary representing the spreading front of the heat. Westudy 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 decayestimates of solutions and the two free boundaries converge to a finite limit for smallinitial data.
Keywords: Nonlinear reaction-advection-diffusion equation; one-phase Stefan problem; decay; blowup.