Random attractors for non-autonomous stochasticwave equations with multiplicative noise

By Bixiang Wang. 2013

246 citations recorded by the source corpus.

This paper is concerned with the asymptotic behavior of solutions of the damped non-autonomous stochastic wave equations driven by multiplicative white noise. We prove the existence of pullback random attractors in $H^1(\mathbb{R}^n) \times L^2(\mathbb{R}^n)$ when the intensity of noise is sufficiently small. We demonstrate that these random attractors are periodic in time if so are the deterministic non-autonomous external terms. We also establish the upper semicontinuity of random attractors when the intensity of noise approaches zero. In addition, we prove the measurability of random attractors even if the underlying probability space is not complete.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Finance

View Paper: https://www.semanticscholar.org/paper/2eb574cfb531f9a5a0de7957666dc07ae9cdc809

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In Computational Theory and Mathematics

1. Bixiang Wang
2. Shengfan Zhou
3. Xiaohu Wang
4. Kening Lu
5. Anhui Gu
6. Min Zhao
7. Renhai Wang
8. Yangrong Li

In Control and Systems Engineering

1. Bixiang Wang
2. Xiaohu Wang
3. Shengfan Zhou
4. Kening Lu
5. Anhui Gu
6. Min Zhao
7. Renhai Wang
8. Peter W. Bates

In Finance

1. Anhui Gu
2. Kening Lu
3. Xiaohu Wang
4. Bixiang Wang
5. Shengfan Zhou
6. Min Zhao

Citations in the corpus

• Exponential Stability of Non-Autonomous Stochastic Delay Lattice Systems with Multiplicative Noise (2015, background): “We remark that the measurability of the attractor A with respect to F was proved in [35] as an improvement of [34].”
• Fractal dimension of random attractor for stochastic non-autonomous damped wave equation with linear multiplicative white noise (2015, background): “[4] P. W. Bates, K. Lu and B. Wang, Random attractors for stochastic reaction-diffusion equations on unbounded domains, J. Differential Equations, 246 (2009), 845–869.”
• Asymptotic behavior of random fitzhugh-nagumo systems driven by colored noise (2017, background): “The concept of random attractors was introduced in [18, 21, 44] and further studied in [6, 7, 8, 9, 11, 12, 13, 15, 16, 18, 22, 23, 24, 26, 32, 37, 40, 50, 51] for the autonomous stochastic equations; and in [2, 14, 19, 27, 28, 52, 53, 54] for the non-autonomous stochastic equations.”