Limiting Behavior of Invariant Measures of Stochastic Delay Lattice Systems

2021 ◽  
Author(s):  
Dingshi Li ◽  
Bixiang Wang ◽  
Xiaohu Wang
Keyword(s):  
Invariant Measures ◽  
Lattice Systems ◽  
Limiting Behavior ◽  
Stochastic Delay

scholarly journals Invariant measures of stochastic delay lattice systems

2017 ◽  
Vol 22 (11) ◽  
pp. 0-0
Author(s):  
Zhang Chen ◽  
◽  
Xiliang Li ◽  
Bixiang Wang ◽  
◽  
...  
Keyword(s):  
Invariant Measures ◽  
Lattice Systems ◽  
Stochastic Delay

UNIFORM ATTRACTORS OF NONAUTONOMOUS DISCRETE REACTION–DIFFUSION SYSTEMS IN WEIGHTED SPACES

2008 ◽  
Vol 18 (03) ◽  
pp. 695-716 ◽  
Author(s):  
BIXIANG WANG
Keyword(s):  
Upper Semicontinuity ◽  
Reaction Diffusion ◽  
Global Attractors ◽  
Weighted Spaces ◽  
Lattice Systems ◽  
Limiting Behavior ◽  
Reaction Diffusion Systems ◽  
Nonautonomous Systems ◽  
Diffusion Systems ◽  
Uniform Attractors

We study the asymptotic behavior of nonautonomous discrete Reaction–Diffusion systems defined on multidimensional infinite lattices. We show that the nonautonomous systems possess uniform attractors which attract all solutions uniformly with respect to the translations of external terms when time goes to infinity. These attractors are compact subsets of weighted spaces, and contain all bounded solutions of the system. The upper semicontinuity of the uniform attractors is established when an infinite-dimensional reaction–diffusion system is approached by a family of finite-dimensional systems. We also examine the limiting behavior of lattice systems with almost periodic, rapidly oscillating external terms in weighted spaces. In this case, it is proved that the uniform global attractors of nonautonomous systems converge to the global attractor of an averaged autonomous system.

Asymptotic analysis and homogenization of invariant measures

2019 ◽  
Vol 19 (02) ◽  
pp. 1950015
Author(s):  
Oleksandr Misiats ◽  
Oleksandr Stanzhytskyi ◽  
Nung Kwan Yip
Keyword(s):  
Asymptotic Behavior ◽  
Invariant Measure ◽  
Stationary Solution ◽  
Invariant Measures ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Regular Case ◽  
Limiting Behavior ◽  
Whole Space

In this paper, we study limiting behavior of the invariant measures for reaction–diffusion equations in the whole space [Formula: see text] with regular and singular perturbations. In the regular case, we show the convergence of the unique stationary solution of [Formula: see text] to a stationary solution of the limiting equation [Formula: see text]. We also consider the asymptotic behavior of the stationary solution under the perturbations of spectrum. Finally, for the singular perturbation of homogenization type, we show the weak convergence of invariant measure to its homogenized limit.

scholarly journals The attractors for 2nd-order stochastic delay lattice systems

2017 ◽  
Vol 37 (1) ◽  
pp. 575-590 ◽  
Author(s):  
Chengjian Zhang ◽  
◽  
Lu Zhao ◽  
Keyword(s):  
Lattice Systems ◽  
Stochastic Delay

Periodic measures of stochastic delay lattice systems

2021 ◽  
Vol 272 ◽  
pp. 74-104
Author(s):  
Dingshi Li ◽  
Bixiang Wang ◽  
Xiaohu Wang
Keyword(s):  
Lattice Systems ◽  
Stochastic Delay

scholarly journals Invariant measures of stochastic Schrödinger delay lattice systems

2021 ◽  
Author(s):  
Chen Zhang ◽  
Wang Bixiang ◽  
Yang Li
Keyword(s):  
Invariant Measures ◽  
Lattice Systems
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