Dynamics of stochastic reaction–diffusion lattice systems driven by nonlinear noise
By Bixiang Wang. Journal of Mathematical Analysis and Applications, 2019
100 citations recorded by the source corpus.
Abstract This paper is concerned with the dynamics of the stochastic reaction–diffusion lattice systems defined on the entire integer set driven by locally Lipschitz nonlinear noise. We prove the existence and uniqueness of solutions as well as weak pullback random attractors for the mean random dynamical systems generated by the solution operators. The existence of invariant measures in l 2 for the stochastic equations is also established. The idea of uniform estimates on the tails of the solutions is employed to show the tightness of a family of probability distributions of the solutions.
Subfields: Computational Theory and Mathematics, Computer Networks and Communications, Control and Systems Engineering
View Paper: https://www.semanticscholar.org/paper/e9769f71a21ee01adf24db1430e6c0bda806001b
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In Computational Theory and Mathematics
In Computer Networks and Communications
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Citations in the corpus
- Limiting Behavior of Invariant Measures of Stochastic Delay Lattice Systems (2021, background): “There is an enormous number of publications on the solutions and their long-term dynamics for lattice systems, which, for instance, can be found in [1–3,7,16,21,27,30,39] for deterministic lattice systems and in [4,5,11,22,31,34,37] for stochastic lattice systems.”
- Invariant measures of stochastic delay lattice systems (2021, background): “, ρ = 0), the existence of invariant measures of stochastic lattice system in `(2) was recently studied in [61, 62] where the uniform tail-estimates are sufficient to derive the tightness of distributions of solutions in `(2).”