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

2007/08/10 by Jean-Philippe Bartier, Bartier, Jean-Philippe, Philippe Laurençot +1 · 1 citation
Computer Science · Mathematics · #35B33 #35B40 #35K65 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.0708.1431

openalex publication_date 2007/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 time goes to infinity of the mass 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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