Blow-up and strong instability of standing waves for the NLS-δ equation on a star graph

被引：12

作者：

Goloshchapova, Nataliia ^{[1
]}

Ohta, Masahito ^{[2
]}

机构：

[1] IME USP, Dept Math, Rua Matao 1010,Cidade Univ, BR-05508090 Sao Paulo, SP, Brazil

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

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2020年 / 196卷

基金：

巴西圣保罗研究基金会;

关键词：

delta- and delta '-interaction; Nonlinear Schrodinger equation; Strong instability; Standing wave; Star graph; Virial identity; NONLINEAR SCHRODINGER-EQUATION; ORBITAL STABILITY; STATES;

D O I：

10.1016/j.na.2020.111753

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study strong instability (by blow-up) of the standing waves for the nonlinear Schrodinger equation with d-interaction on a star graph Gamma. The key ingredient is a novel variational technique applied to the standing wave solutions being minimizers of a specific variational problem. We also show well-posedness of the corresponding Cauchy problem in the domain of the self-adjoint operator which defines d-interaction. This permits to prove virial identity for the H-1-solutions to the Cauchy problem. We also prove certain strong instability results for the standing waves of the NLS-delta' equation on the line. (C) 2020 Elsevier Ltd. All rights reserved.

引用

页数：23

共 21 条

[1] Stable standing waves for a NLS on star graphs as local minimizers of the constrained energy [J].

Adami, Riccardo ;

Cacciapuoti, Claudio ;

Finco, Domenico ;

Noja, Diego .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2016, 260 (10) :7397-7415

[2] Variational properties and orbital stability of standing waves for NLS equation on a star graph [J].

Adami, Riccardo ;

Cacciapuoti, Claudio ;

Finco, Domenico ;

Noja, Diego .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2014, 257 (10) :3738-3777

[3] Stability and Symmetry-Breaking Bifurcation for the Ground States of a NLS with a δ′ Interaction [J].

Adami, Riccardo ;

Noja, Diego .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2013, 318 (01) :247-289

[4] FUNDAMENTAL SOLUTION OF THE HEAT AND SCHRODINGER-EQUATIONS WITH POINT INTERACTION [J].

ALBEVERIO, S ;

BRZEZNIAK, Z ;

DABROWSKI, L .

JOURNAL OF FUNCTIONAL ANALYSIS, 1995, 130 (01) :220-254

[5]

Albeverio S., 2005, Solvable Models in Quantum Mechanics, VSecond

[6]

Angulo J., 2018, DISCRETE CONT DYN-A, V38, P5039

[7]

[Anonymous], 2003, Am. Math. Soc.

[8] DISPERSION FOR THE SCHRODINGER EQUATION ON THE LINE WITH MULTIPLE DIRAC DELTA POTENTIALS AND ON DELTA TREES [J].

Banica, Valeria ;

Ignat, Liviu I. .

ANALYSIS & PDE, 2014, 7 (04) :903-927

[9]

BERESTYCKI H, 1981, CR ACAD SCI I-MATH, V293, P489

[10] Ground state and orbital stability for the NLS equation on a general starlike graph with potentials [J].

Cacciapuoti, Claudio ;

Finco, Domenico ;

Noja, Diego .

NONLINEARITY, 2017, 30 (08) :3271-3303

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