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Existence of the free boundary in a multi-dimensional combustion problem*

Published online by Cambridge University Press:  14 November 2011

Roberto Gianni
Roberto Gianni
Affiliation:
Dipartimento di matematica ‘Ulisse Dini’, Viale Morgagni 67/a 50134, Firenze, Italy
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Extract

In this paper, we consider an n-dimensional semilinear equation of parabolic type with a discontinuous source term arising from combustion theory. We prove local existence for a classical solution having a ‘regular’ free boundary. In this regard, the free boundary is a surface through which the discontinuous source term exhibits a switch-like behaviour. We specify conditions under which this solution and its free boundary are global in time; moreover, we exhibit a special domain for which, for t tending to infinity, such a global-in-time solution converges, together with its free boundary, to the solution of the stationary problem and to its regular free boundary (which is proved to exist), respectively. We also prove uniqueness and continuous dependence theorems.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 125 , Issue 3 , 1995 , pp. 525 - 544
Copyright
Copyright © Royal Society of Edinburgh 1995

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