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.
"Entropy solutions of a combustion model." Commun. Math. Sci. 1 (3) 393 - 407, September 2003.