Title

Random exponential attractor for stochastic discrete long wave-short wave resonance equation with multiplicative white noise

Document Type

Article

Publication Date

8-1-2020

Publication Title

Discrete and Continuous Dynamical Systems - Series B

Volume

25

First Page

3153

Last Page

3170

Keywords

Discrete long wave-short wave resonance equation, Fractal dimension, Multiplicative white noise, Random exponential attractor

Abstract

© 2020 American Institute of Mathematical Sciences. All rights reserved. We mainly consider the existence of a random exponential attractor (positive invariant compact measurable set with finite fractal dimension and attracting orbits exponentially) for stochastic discrete long wave-short wave resonance equation driven by multiplicative white noise. Firstly, we prove the existence of a random attractor of the considered equation by proving the existence of a uniformly tempered pullback absorbing set and making an estimate on the "tails" of solutions. Secondly, we show the Lipschitz property of the solution process generated by the considered equation. Finally, we prove the existence of a random exponential attractor of the considered equation, which implies the finiteness of fractal dimension of random attractor.

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