Regularity of the global attractor for a nonlinear Schrödinger equation with a point defect

Wided Kechiche

doi:10.3934/cpaa.2017060

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2017, Volume 16, Issue 4: 1233-1252. Doi: 10.3934/cpaa.2017060

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Regularity of the global attractor for a nonlinear Schrödinger equation with a point defect

Wided Kechiche

Unité de Recherche Multifractales et Ondelettes, Faculté des Sciences de Monastir, Université de Monastir, Av. de l'environnement, 5000 Monastir, Tunisie

Received: June 2016

Revised: February 2017

Published: May 2017

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Abstract

We consider a nonlinear Schrödinger equation with a delta-function impurity at the origin of the space domain. We study the asymptotic behavior of the solutions with the theory of infinite dynamical system. We first prove the existence of a global attractor in $H^1_0(-1, 1)$. We also establish that this global attractor is a compact subset of $H^{\frac{3}{2}-\epsilon}(-1, 1)$.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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References

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