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The Cauchy problem for the Schrödinger equation in dimension three with concentrated nonlinearity

✍ Scribed by Riccardo Adami; Gianfausto Dell'Antonio; Rodolfo Figari; Alessandro Teta

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
185 KB
Volume
20
Category
Article
ISSN
0294-1449

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✦ Synopsis

We consider the Schrödinger equation in R 3 with nonlinearity concentrated in a finite set of points. We formulate the problem in the space of finite energy V , which is strictly larger than the standard H 1 -space due to the specific singularity exhibited by the solutions. We prove local existence and, for a repulsive or weakly attractive nonlinearity, also global existence of the solutions.

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