Existence of Random Attractors for a Class of Second-Order Lattice Dynamical Systems with Brownian Motions

Yamin Wang, Ziqiao Huang, Fuad E. Alsaadi, Stanislao Lauria, Yurong Liu

Type: Article

Publication Date: 2014-01-01

Citations: 4

DOI: https://doi.org/10.1155/2014/970120

Abstract

This paper is concerned with the random attractors for a class of second-order stochastic lattice dynamical systems. We first prove the uniqueness and existence of the solutions of second-order stochastic lattice dynamical systems in the space<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>F</mml:mi><mml:mo>=</mml:mo><mml:msubsup><mml:mrow><mml:mi>l</mml:mi></mml:mrow><mml:mrow><mml:mi>λ</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup><mml:mo>×</mml:mo><mml:msup><mml:mrow><mml:mi>l</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math>. Then, by proving the asymptotic compactness of the random dynamical systems, we establish the existence of the global random attractor. The system under consideration is quite general, and many existing results can be regarded as the special case of our results.

Locations

Mathematical Problems in Engineering - View - PDF
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Brunel University Research Archive (BURA) (Brunel University London) - View - PDF

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