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Paper   IPM / M / 7343
School of Mathematics
  Title:   Existence of Chapman-Jouguet detonation for a viscous combustion model
  Author(s):  A. Razani
  Status:   Published
  Journal: J. Math. Anal. Appl.
  Vol.:  293
  Year:  2004
  Pages:   551-563
  Supported by:  IPM
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.

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