Blow-up solutions for the Schrödinger equation in dimension three with a concentrated nonlinearity
- 1 February 2004
- journal article
- research article
- Published by European Mathematical Society - EMS - Publishing House GmbH in Annales de l'Institut Henri Poincaré C, Analyse non linéaire
- Vol. 21 (1) , 121-137
- https://doi.org/10.1016/j.anihpc.2003.01.002
Abstract
We present some results on the blow-up phenomenon for the Schrodinger equation in dimension three with a nonlinear term supported in a fixed point. We find sufficient conditions for the blow-up exploiting the moment of inertia of the solution and the uncertainty principle. In the critical case, we discuss the additional symmetries ,of the equation and construct a family of explicit blow-up solutions. (C) 2003 Elsevier SAS. All rights reserved.Keywords
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