Claudia Lederman, Juan Luis Vazquez, & Noemi Wolanski
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 [12] to a more general domain.
As in [12], 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 [11] 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.
Show me the PDF file (166K), TEX file, and other files for this article.
 |
Claudia Lederman Departamento de Matematica Facultad de Ciencias Exactas Universidad de Buenos Aires (1428) Buenos Aires - Argentina e-mail: clederma@dm.uba.ar |
|---|---|
 |
Juan Luis Vazquez Departamento de Matematicas Universidad Autonoma de Madrid 28049 Madrid - Spain e-mail: juanluis.vazquez@uam.es |
 |
Noemi Wolanski Departamento de Matematica Facultad de Ciencias Exactas Universidad de Buenos Aires (1428) Buenos Aires - Argentina e-mail: wolanski@dm.uba.ar |
Return to the EJDE web page