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One-dimensional combustion free boundary problem. (English) Zbl 1086.35152

Summary: A free boundary problem for a parabolic system arising from the mathematical theory of combustion is considered in the one-dimensional case. The existence and uniqueness of the classical solution local in time is obtained by the use of a fixed point theorem. Also the existence of the classical solution global in time and a convergence result with respect to a parameter \(\lambda\) is proved under some reasonable assumptions.

MSC:

35R35 Free boundary problems for PDEs
80A25 Combustion
35K50 Systems of parabolic equations, boundary value problems (MSC2000)
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