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

Ailing Ban; Ailing Ban

doi:10.3934/era.2025200

Electronic Research Archive

2025, Volume 33, Issue 7: 4382-4397. doi: 10.3934/era.2025200

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Research article

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

Ailing Ban ^,

School of Big Data and Artificial Intelligence, Chizhou University, Chizhou 247000, China

Received: 16 March 2025 Revised: 18 June 2025 Accepted: 01 July 2025 Published: 30 July 2025

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.
- random exponential attractor,
- Klein-Gordon-Schrödinger lattice equations,
- multiplicative noise,
- continuous cocycle
Citation: Ailing Ban. Random exponential attractor for a class of non-autonomous stochastic lattice systems[J]. Electronic Research Archive, 2025, 33(7): 4382-4397. doi: 10.3934/era.2025200

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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.

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