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

Valeria Banica

Journées équations aux dérivées partielles (2003)

  • page 1-14
  • ISSN: 0752-0360

Abstract

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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 from below the blow-up rate 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 state 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." Journées équations aux dérivées partielles (2003): 1-14. <http://eudml.org/doc/93443>.

@article{Banica2003,
abstract = {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 from below the blow-up rate 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 state that blow-up cannot occur on the boundary, under certain geometric conditions on the domain.},
author = {Banica, Valeria},
journal = {Journées équations aux dérivées partielles},
keywords = {cubic focusing Schrödinger equation; Dirichlet boundary conditions; plane domain; blow-up rate},
language = {eng},
pages = {1-14},
publisher = {Université de Nantes},
title = {Remarks on the blow-up for the Schrödinger equation with critical mass on a plane domain},
url = {http://eudml.org/doc/93443},
year = {2003},
}

TY - JOUR
AU - Banica, Valeria
TI - Remarks on the blow-up for the Schrödinger equation with critical mass on a plane domain
JO - Journées équations aux dérivées partielles
PY - 2003
PB - Université de Nantes
SP - 1
EP - 14
AB - 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 from below the blow-up rate 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 state that blow-up cannot occur on the boundary, under certain geometric conditions on the domain.
LA - eng
KW - cubic focusing Schrödinger equation; Dirichlet boundary conditions; plane domain; blow-up rate
UR - http://eudml.org/doc/93443
ER -

References

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