Entropy solutions of a combustion model. (English) Zbl 1085.80004

Ying, Lung-An

Commun. Math. Sci. 1, No. 3, 393-407 (2003).

Summary: 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.

MSC:

80A25	Combustion
65M06	Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L65	Hyperbolic conservation laws
65M12	Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
80M20	Finite difference methods applied to problems in thermodynamics and heat transfer

Keywords:

finite difference method; detonation wave; stiff equation; conservation law; combustion; entropy solutions; convergence; projection method