Multi-valued random dynamics of stochastic wave equations with infinite delays

Jingyu Wang; Yejuan Wang; Tomás Caraballo

doi:10.3934/dcdsb.2021310

Article Contents

2022, Volume 27, Issue 10: 6146-6172. Doi: 10.3934/dcdsb.2021310

This issue Previous Article Exponential ergodicity for regime-switching diffusion processes in total variation norm Next Article Statistical solution and Liouville type theorem for coupled Schrödinger-Boussinesq equations on infinite lattices

Multi-valued random dynamics of stochastic wave equations with infinite delays

1.
College of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006, China
2.
School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou 730000, China
3.
Departamento de Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, c/ Tarfia s/n, 41012-Sevilla, Spain

^* Corresponding author
^* Corresponding author

Received: August 2021

Early access: January 2022

Published: October 2022

This work was supported by NSF of China (Grants No. 11801335, 41875084), Scientific and Technologial Innovation Programs of Higher Education Institutions in Shanxi (Grant No. 2020L0249). The research of T. Caraballo has been partially supported by Ministerio de Ciencia Innovación y Universidades (Spain), FEDER (European Community) under grant PGC2018-096540-B-I00, and by FEDER and Junta de Andalucía (Consejería de Economía y Conocimiento) under projects US-1254251 and P18-FR-4509.

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Abstract

This paper is devoted to the asymptotic behavior of solutions to a non-autonomous stochastic wave equation with infinite delays and additive white noise. The nonlinear terms of the equation are not expected to be Lipschitz continuous, but only satisfy continuity assumptions along with growth conditions, under which the uniqueness of the solutions may not hold. Using the theory of multi-valued non-autonomous random dynamical systems, we prove the existence and measurability of a compact global pullback attractor.

Keywords:

Random attractor,
multi-valued non-autonomous random dynamical system,
stochastic delay wave equation,
nonlinear damping,
infinite delay.

Mathematics Subject Classification: Primary: 35L05, 37L30, 37L55.

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References

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