Open AccessThree types of weak pullback attractors for lattice pseudo-parabolic equations driven by locally Lipschitz noise
Author(s) -
Lianbing She,
Nan Liu,
Xin Li,
Renhai Wang
Publication year - 2021
Publication title -
electronic research archive
Language(s) - English
Resource type - Journals
ISSN - 2688-1594
DOI - 10.3934/era.2021028
Subject(s) - lipschitz continuity , mathematics , pullback attractor , uniqueness , attractor , mathematical analysis , nonlinear system , parabolic partial differential equation , random dynamical system , lattice (music) , partial differential equation , physics , linear system , linear dynamical system , quantum mechanics , acoustics
The global well-posedness and long-time mean random dynamics are studied for a high-dimensional non-autonomous stochastic nonlinear lattice pseudo-parabolic equation with locally Lipschitz drift and diffusion terms. The existence and uniqueness of three different types of weak pullback mean random attractors as well as their relations are established for the mean random dynamical systems generated by the solution operators. This is the first paper to study the well-posedness and dynamics of the stochastic lattice pseudo-parabolic equation even when the nonlinear noise reduces to the linear one.