Finite Time Extinction for Nonlinear Schrödinger Equation in 1D and 2D

Rémi Carles, Tohru Ozawa

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

We consider a nonlinear Schrödinger equation with power nonlinearity, either on a compact manifold without boundary, or on the whole space in the presence of harmonic confinement, in space dimension one and two. Up to introducing an extra superlinear damping to prevent finite time blow up, we show that the presence of a sublinear damping always leads to finite time extinction of the solution in 1D, and that the same phenomenon is present in the case of small mass initial data in 2D.

Original languageEnglish
Pages (from-to)897-917
Number of pages21
JournalCommunications in Partial Differential Equations
Volume40
Issue number5
DOIs
Publication statusPublished - 2015 Jan 1

Keywords

  • Asymptotic behavior
  • Finite time extinction
  • Nonlinear Schrödinger equation
  • Nonlinear damping

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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