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|Paper IPM / M / 7343||
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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