
Gradient estimates for a degenerate parabolic equation with gradient absorption and applications
Bartier, Jean-Philippe; Laurençot, Philippe (2007), Gradient estimates for a degenerate parabolic equation with gradient absorption and applications, Journal of Functional Analysis, 254, 3, p. 851-878. http://dx.doi.org/10.1016/j.jfa.2007.10.012
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Type
Article accepté pour publication ou publiéDate
2007Journal name
Journal of Functional AnalysisVolume
254Number
3Publisher
Elsevier
Pages
851-878
Publication identifier
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Show full item recordAbstract (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.Subjects / Keywords
Gradient absorption; p-Laplacian; Localization; Gradient estimates; Temporal decay ratesRelated items
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