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.

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.

@article{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},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     publisher = {Universit\'e de Nantes},
     year = {2003},
     doi = {10.5802/jedp.615},
     zbl = {02079436},
     mrnumber = {2050587},
     language = {en},
     url = {http://www.numdam.org/item/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. http://www.numdam.org/item/JEDP_2003____A1_0/

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