Li, Tong On the initiation problem for a combustion model. (English) Zbl 0808.35073 J. Differ. Equations 112, No. 2, 351-373 (1994). 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. Cited in 8 Documents 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 Keywords:global existence; initiation problem; self-sustaining detonation wave PDFBibTeX XMLCite \textit{T. Li}, J. Differ. Equations 112, No. 2, 351--373 (1994; Zbl 0808.35073) Full Text: DOI