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MiS Preprint
85/2006

Global well-posedness for the Schroedinger equation coupled to a nonlinear oscillator

Alexander Komech and Andrew Komech

Abstract

The Schrödinger equation with the nonlinearity concentrated at a single point proves to be an interesting and important model for the analysis of long-time behavior of solutions, such as the asymptotic stability of solitary waves and properties of weak global attractors. In this note, we prove global well-posedness of this system in the energy space $H\sp 1$.

Received:
23.08.2006
Published:
23.08.2006
MSC Codes:
37K, 35L, 35Q
Keywords:
Schroedinger equation, nonlinear oscillator, global well-posedness

Related publications

inJournal
2007 Repository Open Access
Alexander Komech and Andrew Comech

Global well-posedness for the Schrödinger equation coupled to a nonlinear oscillator

In: Russian journal of mathematical physics, 14 (2007) 2, pp. 164-173