Rigorous asymptotic stability of a Chapman - Jouguet detonation wave in the limit of small resolved heat release

Abstract

We study the rigorous asymptotic stability of a Chapman - Jouguet (CJ) detonation 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 + for initial data which are small perturbations of the CJ detonation wave. A CJ detonation wave is characterized by the property that the speed at the end of it is sonic. A similar phenomenon occurs for a shock profile when the flux function is nonconvex. We use the weighted energy method to overcome the difficulty. The proper choice of the weight cancels the degenerate property of the CJ detonation at the tail. The nonmonotonic part, or the expansive part, of the profile caused by the chemical reaction is treated by the characteristic energy estimate under the assumption of SRHR.