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On the initiation problem for a combustion model. (English) Zbl 0808.35073

Summary: The initiation problem for a combustion model is studied. Global existence of the solution to the problem is established and the asymptotic behavior of the solution is studied. Specifically, we prove that the solution converges to a self-sustaining detonation wave, i.e., the minimal travelling wave, or the CJ detonation wave, followed by a rarefaction wave provided that the initial pulse is large. If the data are small, the solution decays to zero like an \(N\)-wave.

MSC:

35L45 Initial value problems for first-order hyperbolic systems
80A25 Combustion
35B40 Asymptotic behavior of solutions to PDEs
35L67 Shocks and singularities for hyperbolic equations
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