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Smooth solutions to a class of free boundary parabolic problems
Author(s):
Olivier
Baconneau;
Alessandra
Lunardi
Journal:
Trans. Amer. Math. Soc.
356
(2004),
987-1005.
MSC (2000):
Primary 35K05, 35R35
Posted:
October 6, 2003
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Abstract:
We establish existence, uniqueness, and regularity results for solutions to a class of free boundary parabolic problems, including the free boundary heat equation which arises in the so-called ``focusing problem'' in the mathematical theory of combustion. Such solutions are proved to be smooth with respect to time for positive  , if the data are smooth.
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Additional Information:
Olivier
Baconneau
Affiliation:
Division of Mathematics and Computer Science, Free University Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
Email:
olivier@cs.vu.nl
Alessandra
Lunardi
Affiliation:
Dipartimento di Matematica, Università di Parma, Via D'Azeglio 85/A, 43100 Parma, Italy
Email:
lunardi@unipr.it
DOI:
10.1090/S0002-9947-03-03309-9
PII:
S 0002-9947(03)03309-9
Keywords:
Heat equation,
free boundary problems,
fully nonlinear parabolic equations
Received by editor(s):
May 10, 2001
Received by editor(s) in revised form:
July 12, 2002
Posted:
October 6, 2003
Copyright of article:
Copyright
2003,
American Mathematical Society
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