ASYMPTOTIC AUTONOMY OF RANDOM ATTRACTORS FOR BBM EQUATIONS WITH LAPLACE-MULTIPLIER NOISE

Yangrong Li; Renhai Wang

doi:10.11948/20180145

2020 Volume 10 Issue 4

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Yangrong Li, Renhai Wang. ASYMPTOTIC AUTONOMY OF RANDOM ATTRACTORS FOR BBM EQUATIONS WITH LAPLACE-MULTIPLIER NOISE[J]. Journal of Applied Analysis & Computation, 2020, 10(4): 1199-1222. doi: 10.11948/20180145

Citation:

Yangrong Li, Renhai Wang. ASYMPTOTIC AUTONOMY OF RANDOM ATTRACTORS FOR BBM EQUATIONS WITH LAPLACE-MULTIPLIER NOISE[J]. Journal of Applied Analysis & Computation, 2020, 10(4): 1199-1222. doi: 10.11948/20180145

ASYMPTOTIC AUTONOMY OF RANDOM ATTRACTORS FOR BBM EQUATIONS WITH LAPLACE-MULTIPLIER NOISE

Yangrong Li,
Renhai Wang^,

School of Mathematics and Statistics, Southwest University, Chongqing 400715, China

Corresponding author: Email address: liyr@swu.edu.cn(Y. Li)
Fund Project: This work was supported by National Natural Science Foundation of China grant 11571283

Abstract

Abstract

We study asymptotic autonomy of random attractors for possibly non-autonomous Benjamin-Bona-Mahony equations perturbed by Laplacemultiplier noise. We assume that the time-indexed force converges to the time-independent force as the time-parameter tends to negative infinity, and then show that the time-indexed force is backward tempered and backward tail-small. These properties allow us to show that the asymptotic compactness of the non-autonomous system is uniform in the past, and then obtain a backward compact random attractor when the attracted universe consists of all backward tempered sets. More importantly, we prove backward convergence from time-fibers of the non-autonomous attractor to the autonomous attractor. Measurability of solution mapping, absorbing set and attractor is rigorously proved by using Egoroff, Lusin and Riesz theorems.
- Random attractor /
- asymptotic autonomy /
- backward compactness /
- Benjamin-Bona-Mahony equation /
- Laplace-multiplier noise /
- backward tempered set /
- measurability
MSC: 35B40, 37L55, 60H15

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References

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