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Gradient estimates for a degenerate parabolic equation with gradient absorption and applications

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2007-30.pdf (250.4Kb)
Date
2007
Dewey
Analyse
Sujet
Gradient absorption; p-Laplacian; Localization; Gradient estimates; Temporal decay rates
Journal issue
Journal of Functional Analysis
Volume
254
Number
3
Publication date
2008
Article pages
851-878
Publisher
Elsevier
DOI
http://dx.doi.org/10.1016/j.jfa.2007.10.012
URI
https://basepub.dauphine.fr/handle/123456789/6063
Collections
  • CEREMADE : Publications
Metadata
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Author
Bartier, Jean-Philippe
Laurençot, Philippe
Type
Article accepté pour publication ou publié
Abstract (EN)
Qualitative properties of non-negative solutions to a quasilinear degenerate parabolic equation with an absorption term depending solely on the gradient are shown, providing information on the competition between the nonlinear diffusion and the nonlinear absorption. In particular, the limit as t→∞ of the L1-norm of integrable solutions is identified, together with the rate of expansion of the support for compactly supported initial data. The persistence of dead cores is also shown. The proof of these results strongly relies on gradient estimates which are first established.

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