USAChile Workshop on Nonlinear Analysis,
Electron. J. Diff. Eqns., Conf. 06, 2001, pp. 203214.
A mixed semilinear parabolic problem from combustion theory
Claudia Lederman, Juan Luis Vazquez, & Noemi Wolanski
Abstract:
We prove existence, uniqueness, and regularity
of the solution to a mixed initial boundaryvalue problem. The
equation is semilinear uniformly parabolic with principal part in
divergence form, in a noncylindrical spacetime domain.
Here we extend our results in [12] to a more general domain.
As in [12], we assume only mild regularity on the coefficients,
on the noncylindrical 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 noncylindrical 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 [11] to
prove the uniqueness of a ``limit'' solution to the combustion problem
in a twophase situation.
Published January 8, 2001.
Math Subject Classifications: 35K20, 35K60, 80A25.
Key Words: mixed parabolic problem, semilinear parabolic problem,
noncylindrical spacetime domain, combustion.
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Claudia Lederman
Departamento de Matematica
Facultad de Ciencias Exactas
Universidad de Buenos Aires
(1428) Buenos Aires  Argentina
email: clederma@dm.uba.ar 

Juan Luis Vazquez
Departamento de Matematicas
Universidad Autonoma de Madrid
28049 Madrid  Spain
email: juanluis.vazquez@uam.es 

Noemi Wolanski
Departamento de Matematica
Facultad de Ciencias Exactas
Universidad de Buenos Aires
(1428) Buenos Aires  Argentina
email: wolanski@dm.uba.ar 
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