The smoothing property for a class of doubly nonlinear parabolic equations
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- by Carsten Ebmeyer and José Miguel Urbano
- Trans. Amer. Math. Soc. 357 (2005), 3239-3253
- DOI: https://doi.org/10.1090/S0002-9947-05-03790-6
- Published electronically: January 27, 2005
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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.References
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Bibliographic 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
- 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
- © Copyright 2005 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 357 (2005), 3239-3253
- MSC (2000): Primary 35K65; Secondary 35R35, 76S05
- DOI: https://doi.org/10.1090/S0002-9947-05-03790-6
- MathSciNet review: 2135744