Time-Asymptotic Limit of Solutions of a Combustion Problem

A combustion model which captures the interactions among nonlinear convection, chemical reaction and radiative heat transfer is studied. New phenomena are found with radiative heat transfer present. In particular, there is a weak detonation solution for each radiative heat loss coeecient. The speed of the weak detonation wave decreases as the heat loss coeecient increases and the detonation wave does not exist when the heat loss coeecient exceeds a critical value, as expected physically. We study the time-asymptotic limit of solutions of initial value problem for the same problem. We prove that the solution exists globally and the solution converges uniformly, away from the shock, to a shifted traveling wave solution as t! + 1 for certian 'compact support' initial data. Numerical results showing convergence are presented at the end.