Open AccessMulti-valued random dynamics of stochastic wave equations with infinite delays
Author(s) -
Jingyu Wang,
Yejuan Wang,
Tomás Caraballo
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021310
Subject(s) - pullback attractor , uniqueness , lipschitz continuity , attractor , mathematics , white noise , random dynamical system , pullback , nonlinear system , mathematical analysis , wave equation , linear system , physics , linear dynamical system , statistics , quantum mechanics
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.