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.