INHOMOGENEOUS DIRICHLET-BOUNDARY VALUE PROBLEM FOR TWO-DIMENSIONAL QUADRATIC NONLINEAR SCHRODINGER EQUATIONS

被引：2

作者：

Hayashi, Nakao ^{[1
,2
]}

Kaikina, Elena, I ^{[3
]}

机构：

[1] Osaka Univ, Grad Sch Sci, Dept Math, Toyonaka, Osaka 5600043, Japan

[2] Tohoku Univ, Res Alliance Ctr Math Sci, Sendai, Miyagi 9808578, Japan

[3] UNAM, Ctr Ciencias Matemat, Campus Morelia,AP 61-3 Xangari, Morelia 58089, Michoacan, Mexico

来源：

KYUSHU JOURNAL OF MATHEMATICS | 2020年 / 74卷 / 02期

关键词：

nonlinear Schrodinger equation; large-time asymptotics; inhomogeneous initial boundary value problem; upper half-plane; TIME DECAY;

D O I：

10.2206/kyushujm.74.375

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the inhomogeneous Dirichlet boundary value problem for the quadratic nonlinear Schrodinger equations, which is considered as a critical case for the large-time asymptotics of solutions. We present sufficient conditions on the initial and boundary data which ensure asymptotic behavior of small solutions to the equations by using the classical energy method and factorization techniques of the free Schrodinger group.

引用

页码：375 / 400

页数：26

共 27 条

[1] ON THE BOUNDARY VALUE PROBLEM FOR THE SCHRODINGER EQUATION COMPATIBILITY CONDITIONS AND GLOBAL EXISTENCE [J].