Existence of Chapman–Jouguet detonation for a viscous combustion model ✩

In [SIAM J. Appl. Math. 41 (1981) 70–93], Majda proposed a model for the interaction between chemical reactions and compressible fluid dynamics. This model is a low Mach number limit of the one-component reactive Navier–Stokes equations [SIAM J. Appl. Math. 43 (1983) 1086–1118] and was extended to the case where the diffusion coefficient is positive by Larrouturou [Nonlinear Anal. 77 (2001) 405–418]. In this paper, the existence of a one-dimensional Chapman–Jouguet detonation wave, or equivalently a heteroclinic orbit, for the extended model is proven. The proof is based on an application of topological arguments to a system of ordinary differential equations which is obtained from the partial differential equations describing the interaction.  2004 Elsevier Inc. All rights reserved