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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

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

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Author(s):
Goloshchapova, Nataliia [1] ; Ohta, Masahito [2]
Total Authors: 2
Affiliation:
[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
Total Affiliations: 2
Document type: Journal article
Source: NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS; v. 196, JUL 2020.
Web of Science Citations: 0
Abstract

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. (AU)

FAPESP's process: 17/17698-1 - Nonlinear Schrödinger equations with point interactions
Grantee:Jaime Angulo Pava
Support Opportunities: Research Grants - Visiting Researcher Grant - International