Remarks on the blow-up for the Schrödinger equation with critical mass on a plane domain
Journées équations aux dérivées partielles (2003), article no. 1, 14 p.
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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 , the expected one. Moreover, we state that blow-up cannot occur on the boundary, under certain geometric conditions on the domain.
@incollection{JEDP_2003____A1_0,
author = {Banica, Valeria},
title = {Remarks on the blow-up for the {Schr\"odinger} equation with critical mass on a plane domain},
booktitle = {},
series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
eid = {1},
pages = {1--14},
year = {2003},
publisher = {Universit\'e de Nantes},
doi = {10.5802/jedp.615},
mrnumber = {2050587},
zbl = {02079436},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.5802/jedp.615/}
}
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 SP - 1 EP - 14 PB - Université de Nantes UR - http://geodesic.mathdoc.fr/articles/10.5802/jedp.615/ DO - 10.5802/jedp.615 LA - en ID - JEDP_2003____A1_0 ER -
%0 Journal Article %A Banica, Valeria %T Remarks on the blow-up for the Schrödinger equation with critical mass on a plane domain %J Journées équations aux dérivées partielles %D 2003 %P 1-14 %I Université de Nantes %U http://geodesic.mathdoc.fr/articles/10.5802/jedp.615/ %R 10.5802/jedp.615 %G en %F JEDP_2003____A1_0
Banica, Valeria. Remarks on the blow-up for the Schrödinger equation with critical mass on a plane domain. Journées équations aux dérivées partielles (2003), article no. 1, 14 p.. doi: 10.5802/jedp.615
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