Remarks on the blow-up for the Schrödinger equation with critical mass on a plane domain

Valeria Banica[1]

  • [1] Dipartimento di Matematica Università di Pisa Via F. Buonarroti 2 56127 Pisa, Italy

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2004)

  • Volume: 3, Issue: 1, page 139-170
  • ISSN: 0391-173X

Abstract

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In this paper we concentrate on the analysis of the critical mass blowing-up solutions for the cubic focusing Schrödinger equation with Dirichlet boundary conditions, posed on a plane domain. We bound the blow-up rate from below, for bounded and unbounded domains. If the blow-up occurs on the boundary, the blow-up rate is proved to grow faster than ( T - t ) - 1 , the expected one. Moreover, we show that blow-up cannot occur on the boundary, under certain geometric conditions on the domain.

How to cite

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Banica, Valeria. "Remarks on the blow-up for the Schrödinger equation with critical mass on a plane domain." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 3.1 (2004): 139-170. <http://eudml.org/doc/84523>.

@article{Banica2004,
abstract = {In this paper we concentrate on the analysis of the critical mass blowing-up solutions for the cubic focusing Schrödinger equation with Dirichlet boundary conditions, posed on a plane domain. We bound the blow-up rate from below, for bounded and unbounded domains. If the blow-up occurs on the boundary, the blow-up rate is proved to grow faster than $(T-t)^\{-1\}$, the expected one. Moreover, we show that blow-up cannot occur on the boundary, under certain geometric conditions on the domain.},
affiliation = {Dipartimento di Matematica Università di Pisa Via F. Buonarroti 2 56127 Pisa, Italy},
author = {Banica, Valeria},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {1},
pages = {139-170},
publisher = {Scuola Normale Superiore, Pisa},
title = {Remarks on the blow-up for the Schrödinger equation with critical mass on a plane domain},
url = {http://eudml.org/doc/84523},
volume = {3},
year = {2004},
}

TY - JOUR
AU - Banica, Valeria
TI - Remarks on the blow-up for the Schrödinger equation with critical mass on a plane domain
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2004
PB - Scuola Normale Superiore, Pisa
VL - 3
IS - 1
SP - 139
EP - 170
AB - In this paper we concentrate on the analysis of the critical mass blowing-up solutions for the cubic focusing Schrödinger equation with Dirichlet boundary conditions, posed on a plane domain. We bound the blow-up rate from below, for bounded and unbounded domains. If the blow-up occurs on the boundary, the blow-up rate is proved to grow faster than $(T-t)^{-1}$, the expected one. Moreover, we show that blow-up cannot occur on the boundary, under certain geometric conditions on the domain.
LA - eng
UR - http://eudml.org/doc/84523
ER -

References

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