Electronic Journal of Differential Equations,
Conference 06 (2001), pp. 203-214.
Title: A mixed semilinear parabolic problem from combustion theory.
Authors: Claudia Lederman (Univ. de Buenos Aires, Argentina)
Juan Luis Vazquez (Univ. Autonoma de Madrid, Madrid, Spain)
Noemi Wolanski (Univ. de Buenos Aires, Argentina)
Abstract:
We prove existence, uniqueness, and regularity
of the solution to a mixed initial boundary-value problem. The
equation is semilinear uniformly parabolic with principal part in
divergence form, in a non-cylindrical space-time domain.
Here we extend our results in \cite{LVWmix} to a more general domain.
As in \cite{LVWmix}, we assume only mild regularity on the coefficients,
on the non-cylindrical part of the lateral boundary (where the Dirichlet
data are given), and on the Dirichlet data.
This problem is of interest in combustion theory, where
the non-cylindrical part of the lateral boundary may be considered
as an approximation of a flame front.
In particular, the results in this paper are used in \cite{LVWdf} to
prove the uniqueness of a ``limit'' solution to the combustion problem
in a two-phase situation.
Published January 8, 2001.
Math Subject Classifications: 35K20, 35K60, 80A25.
Key Words: mixed parabolic problem; semilinear parabolic problem; non-cylindrical space-time domain; combustion.