Random exponential attractor for a class of non-autonomous stochastic lattice systems

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Abstract

The purpose of this paper was to discuss the existence of a random exponential attractor for non-autonomous coupled Klein-Gordon-Schrödinger (KGS) lattice equations with multiplicative noise. We employed the method of estimation on the tails of solutions to prove the existence of a random attractor for a continuous cocycle generated by the random KGS lattice equations on an infinite-dimensional sequence space, and used this abstract result to prove the Lipschitz continuity of the continuous cocycle. Then, we verified the existence of a random exponential attractor for the investigated system according to a known criterion.

Keywords

random exponential attractor / Klein-Gordon-Schrödinger lattice equations / multiplicative noise / continuous cocycle

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