ASYMPTOTIC BEHAVIOR FOR A SCHRODINGER EQUATION WITH NONLINEAR SUBCRITICAL DISSIPATION

被引：11

作者：

Cazenave, Thierry ^{[1
,2
]}

Han, Zheng ^{[3
]}

机构：

[1] Sorbonne Univ, BC 187,4 Pl Jussieu, F-75252 Paris 05, France

[2] CNRS, Lab Jacques Louis Lions, BC 187,4 Pl Jussieu, F-75252 Paris 05, France

[3] Hangzhou Normal Univ, Dept Math, 2318 Yuhangtang Rd, Hangzhou 311121, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2020年 / 40卷 / 08期

关键词：

Nonlinear Schrodinger equation; subcritical dissipative nonlinearity; asymptotic behavior; LOW-ENERGY; SCATTERING; BLOWUP;

D O I：

10.3934/dcds.2020202

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the time-asymptotic behavior of solutions of the Schrodinger equation with nonlinear dissipation partial derivative(t)u = i Delta u + lambda vertical bar u vertical bar(alpha)u in R-N, N >= 1, where lambda is an element of C, R lambda < 0 and 0 < alpha < 2/N. We give a precise description of the behavior of the solutions (including decay rates in L-2 and L-infinity, and asymptotic profile), for a class of arbitrarily large initial data, under the additional assumption that alpha is sufficiently close to 2/N.

引用

页码：4801 / 4819

页数：19

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