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Blow-up solutions for the Schrödinger equation in dimension three with a concentrated nonlinearity

TitleBlow-up solutions for the Schrödinger equation in dimension three with a concentrated nonlinearity
Publication TypeJournal Article
Year of Publication2004
AuthorsAdami, R, Dell'Antonio, G, Figari, R, Teta, A
JournalAnn. Inst. H. Poincare Anal. Non Lineaire 21 (2004) 121-137
Abstract

We present some results on the blow-up phenomenon for the Schroedinger 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 symmetry of the equation and construct a family of explicit blow up solutions.

URLhttp://hdl.handle.net/1963/2998
DOI10.1016/j.anihpc.2003.01.002

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