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

Bartier, Jean-Philippe; Laurençot, Philippe

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 publié

Date

2007

Journal name

Journal of Functional Analysis

Volume

254

Number

Publisher

Elsevier

Pages

851-878

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.

Subjects / Keywords

Gradient absorption; p-Laplacian; Localization; Gradient estimates; Temporal decay rates