Pullback attractors and invariant measures for discrete Klein-Gordon-Schrödinger equations

Caidi Zhao; Gang Xue; Grzegorz Łukaszewicz

doi:10.3934/dcdsb.2018122

Article Contents

2018, Volume 23, Issue 9: 4021-4044. Doi: 10.3934/dcdsb.2018122

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Pullback attractors and invariant measures for discrete Klein-Gordon-Schrödinger equations

1.
College of Mathematical Physics and Electronic Information Engineering, Wenzhou University, Wenzhou 325035, China
2.
Institute of Applied Mathematics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland

* Corresponding author: Caidi Zhao
* Corresponding author: Caidi Zhao

Received: May 31, 2017

Revised: November 30, 2017

Early access: April 2018

Published: September 2018

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Abstract

In this article, we first provide a sufficient and necessary condition for the existence of a pullback-$ {\mathcal D} $ attractor for the process defined on a Hilbert space of infinite sequences. As an application, we investigate the non-autonomous discrete Klein-Gordon-Schrödinger system of equations, prove the existence of the pullback-$ {\mathcal D} $ attractor and then the existence of a unique family of invariant Borel probability measures associated with the considered system.

Keywords:

Non-autonomous lattice system,
pullback attractor,
invariant measures,
discrete Klein-Gordon-Schrödinger equations.

Mathematics Subject Classification: 35B41, 35D99, 76F20.

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