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A qualitative model for studying shock-wave chemistry interactions in combustion theory is introduced. The model studied bears the analogous relationship to reacting gas flow as Burgers' equation does to ordinary compressible fluid flow. When the corresponding physical assumptions of the Chapman-Jouget and von Heumann-Zeldovich-Doring theories are introduced in this model, explicit and completely analogous phenomena occur. Without any approximations, combustion profiles with finite reaction rate and finite diffusion are examined in detail. In the context of this model, the validity of the approximate theories mentioned above depends on the relative size of two critical parameters - the energy liberated by chemical reaction and a parameter which measures the ratio of the width of the shock layer to the reaction zone.

Original languageEnglish (US)
Pages (from-to)70-93
Number of pages24
JournalSIAM Journal on Applied Mathematics
Issue number1
StatePublished - 1981

ASJC Scopus subject areas

  • Applied Mathematics

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