UPPER AND LOWER L2-DECAY BOUNDS FOR A CLASS OF DERIVATIVE NONLINEAR SCHRODINGER EQUATIONS

被引：2

作者：

Li, Chunhua ^{[1
]}

Nishii, Yoshinori ^{[2
]}

Sagawa, Yuji ^{[3
]}

Sunagawa, Hideaki ^{[4
]}

机构：

[1] Yanbian Univ, Coll Sci, Dept Math, 977 Gongyuan Rd, Jilin, Peoples R China

[2] Tokyo Univ Sci, Dept Math, 1-3 Kagurazaka, Tokyo, Tokyo 1628601, Japan

[3] Chiba Inst Technol, Dept Math, 2-1-1 Shibazono, Narashino, Chiba 2750023, Japan

[4] Osaka Metropolitan Univ, Grad Sch Sci, Dept Math, 3-3-138 Sugimoto, Sumiyoshi, Osaka 5588585, Japan

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2022年

关键词：

Derivative nonlinear Schrö dinger equation; weakly dissipative structure; optimal L-2-decay rate; LARGE TIME ASYMPTOTICS; DISSIPATIVE NONLINEARITY; DECAY-RATES; LIFE-SPAN; BEHAVIOR; SYSTEM;

D O I：

10.3934/dcds.2022129

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the initial value problem for cubic derivative nonlinear Schrodinger equations possessing weakly dissipative structure in one space dimension. We show that the small data solution decays like O((log t)(-1/4)) in L-2 as t -> +infinity. Furthermore, we find that this L-2-decay rate is optimal by giving a lower estimate of the same order.

引用

页码：5893 / 5908

页数：16

共 28 条

[1] Asymptotic behavior for a dissipative nonlinear Schrodinger [J].

Cazenave, Thierry ;

Han, Zheng ;

Naumkin, Ivan .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2021, 205

[2] ASYMPTOTIC BEHAVIOR FOR A SCHRODINGER EQUATION WITH NONLINEAR SUBCRITICAL DISSIPATION [J].

Cazenave, Thierry ;

Han, Zheng .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2020, 40 (08) :4801-4819

[3] Asymptotics for large time of solutions to the nonlinear Schrodinger and Hartree equations [J].

Hayashi, N ;

Naumkin, PI .

AMERICAN JOURNAL OF MATHEMATICS, 1998, 120 (02) :369-389

[4]

Hayashi N., 2002, INT J PURE APPL MATH, V3, P255

[5] On the Schrodinger equation with dissipative nonlinearities of derivative type [J].

Hayashi, Nakao ;

Naumkin, Pavel I. ;

Sunagawa, Hideaki .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2008, 40 (01) :278-291

[6] UPPER AND LOWER TIME DECAY BOUNDS FOR SOLUTIONS OF DISSIPATIVE NONLINEAR SCHRODINGER EQUATIONS [J].

Hayashi, Nakao ;

Li, Chunhua ;

Naumkin, Pavel I. .

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2017, 16 (06) :2089-2104

[7] Time Decay for Nonlinear Dissipative Schrodinger Equations in Optical Fields [J].

Hayashi, Nakao ;

Li, Chunhua ;

Naumkin, Pavel I. .

ADVANCES IN MATHEMATICAL PHYSICS, 2016, 2016

[8] Asymptotic behavior for solutions to the dissipative nonlinear Scrodinger equations with the fractional Sobolev space [J].

Hoshino, Gaku .

JOURNAL OF MATHEMATICAL PHYSICS, 2019, 60 (11)

[9] DISSIPATIVE NONLINEAR SCHRODINGER EQUATIONS FOR LARGE DATA IN ONE SPACE DIMENSION [J].

Hoshino, Gaku .

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2020, 19 (02) :967-981

[10] The initial value problem for nonlinear Schrodinger equations with a dissipative nonlinearity in one space dimension [J].

Jin, Guangzhi ;

Jin, Yuanfeng ;

Li, Chunhua .

JOURNAL OF EVOLUTION EQUATIONS, 2016, 16 (04) :983-995

← 1 2 3 →