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

Nataliia Goloshchapova, Masahito Ohta

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Abstract

We study strong instability (by blow-up) of the standing waves for the nonlinear Schrödinger equation with δ-interaction on a star graph Γ. 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 δ-interaction. This permits to prove virial identity for the H1-solutions to the Cauchy problem. We also prove certain strong instability results for the standing waves of the NLS-δ equation on the line.

Original languageEnglish
Article number111753
JournalNonlinear Analysis, Theory, Methods and Applications
Volume196
DOIs
Publication statusPublished - Jul 2020

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Keywords

  • Nonlinear Schrödinger equation
  • Standing wave
  • Star graph
  • Strong instability
  • Virial identity
  • δ- and δ-interaction

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