Asymptotics of blowup for a convection-diffusion equation with conservation

Abstract

This paper deals with a parabolic partial differential equation that incorporates diffusion and convection terms and that previously has been shown to have solutions that become unbounded at a single point in finite time. The results presented here describe the limiting behavior of the solution in a neighborhood of the blowup point, as well as the asymptotic growth rate as the blowup time is approached. Rigorous estimates are proved, and some supplementary numerical calculations are presented.