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Limiting Behavior of Random Attractors of Stochastic Supercritical Wave Equations Driven by Multiplicative Noise.

Authors :
Chen, Zhang
Wang, Bixiang
Source :
Applied Mathematics & Optimization. Oct2023, Vol. 88 Issue 2, p1-32. 32p.
Publication Year :
2023

Abstract

This paper deals with the limiting behavior of random attractors of stochastic wave equations with supercritical drift driven by linear multiplicative white noise defined on unbounded domains. We first establish the uniform Strichartz estimates of the solutions with respect to noise intensity, and then prove the convergence of the solutions of the stochastic equations with respect to initial data as well as noise intensity. To overcome the non-compactness of Sobolev embeddings on unbounded domains, we first utilize the uniform tail-ends estimates to truncate the solutions in a bounded domain and then employ a spectral decomposition to establish the pre-compactness of the collection of all random attractors. We finally prove the upper semicontinuity of random attractor as noise intensity approaches zero. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
00954616
Volume :
88
Issue :
2
Database :
Academic Search Index
Journal :
Applied Mathematics & Optimization
Publication Type :
Academic Journal
Accession number :
169936477
Full Text :
https://doi.org/10.1007/s00245-023-10030-4