LARGE TIME BEHAVIOR FOR A NONLOCAL NONLINEAR GRADIENT FLOW

被引：2
|
作者：
Li, Feng [1 ]
Lindgren, Erik [1 ]
机构：
[1] Uppsala Univ, Dept Math, Box 480, S-75106 Uppsala, Sweden
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2022年
基金：
瑞典研究理事会;
关键词：
Nonlocal parabolic equations; fractional p-Laplacian; asymptotic behavior; sharp decay; Moser iteration; FRACTIONAL P-LAPLACIAN; PARABOLIC EQUATIONS;
D O I：
10.3934/dcds.2022079
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the large time behavior of the nonlinear and nonlocal equation v(t) + (-Delta(p))(s) v = f, where p is an element of (1, 2) boolean OR (2, infinity), s is an element of (0, 1) and (-Delta(p))(s) v(x, t) = 2 P.V. integral(Rn) vertical bar v(x, t) - v(x + y, t)vertical bar(p-2)(v(x, t) - v(x + y, t))/vertical bar y vertical bar(n+sp) dy. This equation arises as a gradient flow in fractional Sobolev spaces. We obtain sharp decay estimates as t -> infinity. The proofs are based on an iteration method in the spirit of J. Moser previously used by P. Juutinen and P. Lindqvist.
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页码：1516 / 1546
页数：31
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