Long time behavior of solutions to a Schrödinger-Poisson system in $R^3$

Amna  Dabaa; O. Goubet

doi:10.3934/cpaa.2016011

Article Contents

2016, Volume 15, Issue 5: 1743-1756. Doi: 10.3934/cpaa.2016011

This issue Previous Article A new proof of gradient estimates for mean curvature equations with oblique boundary conditions Next Article Global and blowup solutions for general Lotka-Volterra systems

Long time behavior of solutions to a Schrödinger-Poisson system in $R^3$

Amna Dabaa^1, and
O. Goubet^2,

1.
LAMFA CNRS UMR 7352, Université de Picardie Jules Verne, 33 rue Saint-Leu 80039 Amiens cedex
2.
LAMFA CNRS UMR 6140, Université de Picardie Jules Verne, 33 rue Saint-Leu 80039 Amiens cedex

Received: August 31, 2015

Revised: February 29, 2016

Published: August 2016

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Abstract

We consider a damped forced nonlinear Schrödinger-Poisson system in $R^3$. This provides us with an infinite-dimensional dynamical system in the energy space $H^1(R^3)$. We prove the existence of a finite dimensional global attractor for this dynamical system.

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Mathematics Subject Classification: Primary: 35B41, 35B40, 35M30, 35Q55.

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References

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