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

Autor(es)

Goloshchapova, Nataliia ^[1] ; Ohta, Masahito ^[2]

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS; v. 196, JUL 2020.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 17/17698-1 - Equações de Schrödinger não-linear com pontos de interação
• Beneficiário: Jaime Angulo Pava
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional