Smoothing effect and large time behavior of solutions to Schrodinger equations with nonlinearity of integral type

被引：3

作者：

Ozawa, T ^{[1
]}

Yamazaki, Y ^{[1
]}

机构：

[1] Hokkaido Univ, Dept Math, Sapporo, Hokkaido 0600810, Japan

来源：

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS | 2004年 / 6卷 / 04期

关键词：

nonlinear Schrodinger equation; scattering;

D O I：

10.1142/S0219199704001458

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the smoothing effect in space and asymptotic behavior in time of solutions to the Cauchy problem for the nonlinear Schrodinger equation with interaction described by the integral of the intensity with respect to one direction in two space dimensions. A detailed description is given on the phase modification of scattering solutions by taking into account the long range effect of the interaction.

引用

下载

页码：681 / 703

页数：23

共 50 条

[1] Analytic smoothing effect for solutions to Schrodinger equations with nonlinearity of integral type
Ozawa, T
Yamauchi, K
Yamazaki, Y
OSAKA JOURNAL OF MATHEMATICS, 2005, 42 (04) : 737 - 750
[2] Large time behavior of solutions to Schrodinger equations with a dissipative nonlinearity for arbitrarily large initial data
Kita, Naoyasu
Shimomura, Akihiro
JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 2009, 61 (01) : 39 - 64
[3] Analyticity in time and smoothing effect of solutions to nonlinear Schrodinger equations
Hayashi, N
Kato, K
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1997, 184 (02) : 273 - 300
[4] Smoothing effect and exponential time decay of solutions of Schrodinger equations
Dan, Y
Kajitani, K
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 2002, 78 (06) : 92 - 95
[5] Space-Time Analytic Smoothing Effect for Global Solutions to a System of Nonlinear Schrodinger Equations with Large Data
Hoshino, Gaku
ANNALES HENRI POINCARE, 2018, 19 (07): : 2101 - 2114
[6] Smoothing effect and large time behavior of solutions to nonlinear elastic wave equations with viscoelastic term
Kagei, Yoshiyuki
Takeda, Hiroshi
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2022, 219
[7] Large time behavior of solutions for derivative cubic nonlinear Schrodinger equations
Hayashi, N
Naumkin, PI
Uchida, H
PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, 1999, 35 (03) : 501 - 513
[8] Asymptotic behavior of solutions to Schrodinger equations with a subcritical dissipative nonlinearity
Kita, Naoyasu
Shimomura, Akihiro
JOURNAL OF DIFFERENTIAL EQUATIONS, 2007, 242 (01) : 192 - 210
[9] Analytic smoothing effect for global solutions to nonlinear Schrodinger equations
Ozawa, T.
Yamauchi, K.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2010, 364 (02) : 492 - 497
[10] SCHRODINGER EQUATION WITH NONLINEARITY OF INTEGRAL TYPE
BAILLON, JB
CAZENAVE, T
FIGUEIRA, M
COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES SERIE A, 1977, 284 (16): : 939 - 942

← 1 2 3 4 5 →