Entropy solutions of a combustion model

We study weak solutions to a combustion model problem. An equivalent conservation law with discontinuous flux is derived. Definition of an entropy solution is given, and the existence and uniqueness of the entropy solutions is proved. The convergence of a projection method and an implicit finite difference scheme is also proved. Finally using this approach we prove the convergence of a random projection method.

Keywords

combustion, finite difference method, detonation wave, stiff equation, conservation law

2010 Mathematics Subject Classification

35L65, 65M06, 76M20, 80A25

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Published 1 January 2003