Asymptotic behavior for a singular diffusion equation with gradient absorption

被引：4
|
作者：
Iagar, Razvan Gabriel [1 ,2 ]
Laurencot, Philippe [3 ]
机构：
[1] Univ Valencia, Dept Anal Matemat, E-46100 Burjassot, Valencia, Spain
[2] Romanian Acad, Inst Math, RO-014700 Bucharest, Romania
[3] Univ Toulouse, CNRS, Inst Math Toulouse, UMR 5219, F-31062 Toulouse 9, France
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2014年 / 256卷 / 08期
关键词：
Large time behavior; Singular diffusion; Gradient absorption; Very singular solutions; p-Laplacian; Bounded measures; DEGENERATE PARABOLIC EQUATION; HAMILTON-JACOBI EQUATIONS; CAUCHY-PROBLEM; P-LAPLACIAN; EXTINCTION; UNIQUENESS;
D O I：
10.1016/j.jde.2014.01.016
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the large time behavior of non-negative solutions to the singular diffusion equation with gradient absorption partial derivative(t)u - Delta(p)u + vertical bar del u vertical bar(q) = 0 in (0,infinity) x R-N, for p(c) := 2N/(N + 1) < p < 2 and p/2 < q < q(*) := p-N/(N + 1). We prove that there exists a unique very singular solution of the equation, which has self-similar form and we show the convergence of general solutions with suitable initial data towards this unique very singular solution. (C) 2014 Elsevier Inc. All rights reserved.
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页码：2739 / 2777
页数：39
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