Yi, Fahuai One-dimensional combustion free boundary problem. (English) Zbl 1086.35152 Glasg. Math. J. 46, No. 1, 63-75 (2004). 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. Cited in 7 Documents MSC: 35R35 Free boundary problems for PDEs 80A25 Combustion 35K50 Systems of parabolic equations, boundary value problems (MSC2000) Keywords:existence; uniqueness; classical solution local in time; fixed point theorem; classical solution global in time PDFBibTeX XMLCite \textit{F. Yi}, Glasg. Math. J. 46, No. 1, 63--75 (2004; Zbl 1086.35152) Full Text: DOI