Riemann problem for gasdynamic combustion

Tong Zhang, Yuxi Zheng

Research output: Contribution to journalArticlepeer-review

29 Scopus citations


The Riemann problem for gasdynamic combustion is considered. Existence and uniqueness are obtained constructively for arbitrary Riemann data under the following restrictions: the solutions are selfsimilar and piecewise smooth; the Lax entropy condition is satisfied at the discontinuity points except at the front sides of deflagration waves where the temperatures are assumed to be ignition point; the number of detonation waves in the solutions is as small as possible; the number of times of oscillation of temperature around the ignition point is also as small as possible; and last, the number of deflagration waves is as large as possible. Using the Riemann problem, we analyzed the overtaking of shocks and combustion waves: a shock always accelerates detonation, whereas it transforms deflagration into detonation when it is strong enough. Transition from deflagration to detonation in the ignition problem is also investigated.

Original languageEnglish (US)
Pages (from-to)203-230
Number of pages28
JournalJournal of Differential Equations
Issue number2
StatePublished - Feb 1989

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics


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