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.

引用

页码：1516 / 1546

页数：31