The Cauchy problem for the Schrodinger equation in dimension three with concentrated nonlinearity

被引：41

作者：

Adami, R

Dell'Antonio, G

Figari, R

Teta, A

机构：

[1] Ecole Normale Super, Dept Math & Applicat, F-75231 Paris, France

[2] Univ Roma La Sapienza, Dipartimento Matemat, I-00185 Rome, Italy

[3] SISSA, ISAS, Lab Interdisciplinare, I-34014 Trieste, Italy

[4] Univ Naples Federico II, Dipartimento Sci Fis, Naples, Italy

[5] Univ Aquila, Dipartimento Matemat Pura & Applicata, I-67100 Laquila, Italy

来源：

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2003年 / 20卷 / 03期

关键词：

Nonlinear Schrodinger Equation (NLSE); point interactions; nonlinear Dirac Delta potentials; existence and uniqueness in energy space;

D O I：

10.1016/S0294-1449(02)00022-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the Schrodinger equation in R-3 with nonlinearity concentrated in a finite set of points. We formulate the problem in the space of finite energy V, which is strictly larger than the standard H-1-space due to the specific singularity exhibited by the solutions. We prove local existence and, for a repulsive or weakly attractive nonlinearity, also global existence of the solutions. (C) 2003 Editions scientifiques et medicales Elsevier SAS.

引用

页码：477 / 500

页数：24

共 15 条

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Adami R, 1999, OPER THEOR, V108, P183

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