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