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

Xingni Tan; Fuqi Yin; Guihong Fan

doi:10.3934/dcdsb.2020055

Article Contents

2020, Volume 25, Issue 8: 3153-3170. Doi: 10.3934/dcdsb.2020055

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

1.
School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan 411105, China
2.
Hunan Defense Industry Polytechnic, Xiangtan, Hunan 411207, China
3.
Department of Mathematics, Columbus State University, Columbus, Georgia 31907, USA

^* Corresponding author: Fuqi Yin
^* Corresponding author: Fuqi Yin

Received: April 30, 2019

Revised: August 31, 2019

Early access: February 2020

Published: August 2020

The corresponding author is supported by The Scientific Research Foundation Funded by Hunan Provincial Education Department under grant 19A503 and 15K127; partially supported by Hunan Provincial Natural Science Foundation of China under grant 2015JJ2144, National Natural Science Foundation of People’s Republic of China under grant 11671343

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Abstract

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.

Keywords:

Random exponential attractor,
fractal dimension,
multiplicative white noise,
discrete long wave-short wave resonance equation.

Mathematics Subject Classification: 37L55; 35B40; 60H15.

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References

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