Smooth solutions to a class of free boundary parabolic problems

Baconneau, Olivier; Lunardi, Alessandra

doi:10.1090/S0002-9947-03-03309-9

Smooth solutions to a class of free boundary parabolic problems
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by Olivier Baconneau and Alessandra Lunardi PDF

Trans. Amer. Math. Soc. 356 (2004), 987-1005 Request permission

Abstract:

We establish existence, uniqueness, and regularity results for solutions to a class of free boundary parabolic problems, including the free boundary heat equation which arises in the so-called “focusing problem” in the mathematical theory of combustion. Such solutions are proved to be smooth with respect to time for positive $t$, if the data are smooth.

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