ONE DIMENSIONAL COMBUSTION FREE BOUNDARY PROBLEM The project supported by the National Natural Science Foundation of China (No. 10371045) and Guangdong Provincial Natural Science Foundation of China (No. 000671).

Abstract

Abstract.A free boundary problem for a parabolic system arising from the mathematical theory of combustion will be considered in the one dimensional case. The existence and uniqueness of the classical solution locally in time will be obtained by the use of a fixed point theorem. Also the existence of the classical solution globally in time and a convergence result with respect to a parameter λ will be proved under some reasonable assumptions.2000 Mathematics Subject Classification. 35R35.