Semi discrete weakly damped nonlinear Klein-Gordon Schrödinger system

Olivier Goubet; Marilena N. Poulou

doi:10.3934/cpaa.2014.13.1525

Article Contents

2014, Volume 13, Issue 4: 1525-1539. Doi: 10.3934/cpaa.2014.13.1525

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Semi discrete weakly damped nonlinear Klein-Gordon Schrödinger system

Olivier Goubet^1, and
Marilena N. Poulou^2,

1.
LAMFA, UMR CNRS 7352, Université de Picardie Jules Verne, 33 rue St Leu, 80039, Amiens Cedex
2.
Department of Mathematics, National Technical University, Zografou Campus 157 80, Athens

Received: June 30, 2013

Revised: November 30, 2013

Published: June 2015

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Abstract

We consider a semi-discrete in time relaxation scheme to discretize a damped forced nonlinear Klein-Gordon Schrödinger system. This provides us with a discrete infinite-dimensional dynamical system. We prove the existence of a finite dimensional global attractor for this dynamical system.

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Mathematics Subject Classification: Primary: 35Q55, 37L30.

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