# American Institute of Mathematical Sciences

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January  2022, 27(1): 73-101. doi: 10.3934/dcdsb.2021033

## Approximate dynamics of a class of stochastic wave equations with white noise

 1 School of Mathematical Science, and V.C. & V.R. Key Lab, Sichuan Normal University, Chengdu, 610068, China 2 College of Management Science, Chengdu University of Technology, Chengdu, 610059, China

* Corresponding author: Guanggan Chen

Received  August 2020 Revised  November 2020 Published  January 2022 Early access  February 2021

Fund Project: The first author is supported by the National Science Foundation of China (Grants No. 11571245)

This work is concerned with a stochastic wave equation driven by a white noise. Borrowing from the invariant random cone and employing the backward solvability argument, this wave system is approximated by a finite dimensional wave equation with a white noise. Especially, the finite dimension is explicit, accurate and determined by the coefficient of this wave system; and further originating from an Ornstein-Uhlenbek process and applying Banach space norm estimation, this wave system is approximated by a finite dimensional wave equation with a smooth colored noise.

Citation: Guanggan Chen, Qin Li, Yunyun Wei. Approximate dynamics of a class of stochastic wave equations with white noise. Discrete & Continuous Dynamical Systems - B, 2022, 27 (1) : 73-101. doi: 10.3934/dcdsb.2021033
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