Communications on Pure and Applied Analysis (CPAA)

Semi discrete weakly damped nonlinear Klein-Gordon Schrödinger system

Pages: 1525 - 1539, Volume 13, Issue 4, July 2014      doi:10.3934/cpaa.2014.13.1525

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Olivier Goubet - LAMFA, UMR CNRS 7352, Université de Picardie Jules Verne, 33 rue St Leu, 80039, Amiens Cedex, France (email)
Marilena N. Poulou - Department of Mathematics, National Technical University, Zografou Campus 157 80, Athens, Greece (email)

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.

Keywords:  Klein-Gordon Schrödinger system, global attractor, fractal dimension, relaxation scheme.
Mathematics Subject Classification:  Primary: 35Q55, 37L30.

Received: July 2013;      Revised: December 2013;      Available Online: February 2014.