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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The smoothing property for a class of doubly nonlinear parabolic equations


Authors: Carsten Ebmeyer and José Miguel Urbano
Journal: Trans. Amer. Math. Soc. 357 (2005), 3239-3253
MSC (2000): Primary 35K65; Secondary 35R35, 76S05
Published electronically: January 27, 2005
MathSciNet review: 2135744
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Abstract: We consider a class of doubly nonlinear parabolic equations used in modeling free boundaries with a finite speed of propagation. We prove that nonnegative weak solutions satisfy a smoothing property; this is a well-known feature in some particular cases such as the porous medium equation or the parabolic $p$-Laplace equation. The result is obtained via regularization and a comparison theorem.


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Additional Information

Carsten Ebmeyer
Affiliation: Mathematisches Seminar, Universität Bonn, Nussallee 15, D-53115 Bonn, Germany
Email: cebmeyer@uni-bonn.de

José Miguel Urbano
Affiliation: Departamento de Matemática, Universidade de Coimbra, 3001-454 Coimbra, Portugal
Email: jmurb@mat.uc.pt

DOI: http://dx.doi.org/10.1090/S0002-9947-05-03790-6
PII: S 0002-9947(05)03790-6
Keywords: Degenerate parabolic equation, free boundary, finite speed of propagation, porous medium equation
Received by editor(s): November 12, 2002
Received by editor(s) in revised form: November 19, 2003
Published electronically: January 27, 2005
Additional Notes: The second author was supported in part by the Project FCT-POCTI/34471/MAT/2000 and CMUC/FCT
Article copyright: © Copyright 2005 American Mathematical Society