RIGOROUS ASYMPTOTIC STABILITY OF A CHAPMAN-JOUGUET DETONATION-WAVE INTHE LIMIT OF SMALL RESOLVED HEAT RELEASE

We study the rigorous asymptotic stability of a Chapman-Jouguet (CI) d etonation wave in the limit of small resolved heat release (SRHR). We show that the solution exists globally and that the solution converges uniformly to a shifted CJ detonation wave as t --> +infinity for init ial data which are small perturbations of the CI detonation wave. A CJ detonation wave is characterized by the property that the speed at th e end of it is sonic. A similar phenomenon occurs for a shock profile when the Bur function is nonconvex. We use the weighted energy method to overcome the difficulty. The proper choice of the weight cancels th e degenerate property of the CI detonation at the tail. The nonmonoton ic part, or the expansive part, of the profile caused by the chemical reaction is treated by the characteristic energy estimate under the as sumption of SRHR.