2001 A mixed semilinear parabolic problem in a noncylindrical space-time domain
C. Lederman, J. L. Vazquez, Noemi Wolanski
Differential Integral Equations 14(4): 385-404 (2001). DOI: 10.57262/die/1356123313


In this paper we prove existence, uniqueness and regularity of the solution to a mixed initial-boundary value problem for a semilinear uniformly parabolic equation with principal part in divergence form, in a noncylindrical space-time domain. We assume only mild regularity on the coefficients and on the non-cylindrical part of the lateral boundary (on which Dirichlet data are given). Also, we assume only mild regularity on the Dirichlet data. We consider two different situations, one with a bounded domain and one with an unbounded domain. This problem is of interest in combustion theory. In that situation, the noncylindrical part of the lateral boundary may be considered as an approximation of a flame front. The second order part of the equation is the Laplace operator. In particular, the results in this paper are used in [8] to prove the uniqueness of a ``limit'' solution to the combustion problem.


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C. Lederman. J. L. Vazquez. Noemi Wolanski. "A mixed semilinear parabolic problem in a noncylindrical space-time domain." Differential Integral Equations 14 (4) 385 - 404, 2001. https://doi.org/10.57262/die/1356123313


Published: 2001
First available in Project Euclid: 21 December 2012

zbMATH: 1011.35067
MathSciNet: MR1799414
Digital Object Identifier: 10.57262/die/1356123313

Primary: 35K55
Secondary: 35D05 , 35D10 , 35K60 , 35K65

Rights: Copyright © 2001 Khayyam Publishing, Inc.


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Vol.14 • No. 4 • 2001
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