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Smooth solutions to a class of free boundary parabolic problems


Authors: Olivier Baconneau and Alessandra Lunardi
Journal: Trans. Amer. Math. Soc. 356 (2004), 987-1005
MSC (2000): Primary 35K05, 35R35
DOI: https://doi.org/10.1090/S0002-9947-03-03309-9
Published electronically: October 6, 2003
MathSciNet review: 1984464
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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 $t$, 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: https://doi.org/10.1090/S0002-9947-03-03309-9
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
Published electronically: October 6, 2003
Article copyright: © Copyright 2003 American Mathematical Society

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