Attractors of stochastic lattice dynamical systems with a multiplicative noise and non-Lipschitz nonlinearities
By Tomás Caraballo, Francisco Morillas, José Valero. 2012
141 citations recorded by the source corpus.
Abstract In this paper we study the asymptotic behavior of solutions of a first-order stochastic lattice dynamical system with a multiplicative noise. We do not assume any Lipschitz condition on the nonlinear term, just a continuity assumption together with growth and dissipative conditions, so that uniqueness of the Cauchy problem fails to be true. Using the theory of multi-valued random dynamical systems we prove the existence of a random compact global attractor.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering
View Paper: https://www.semanticscholar.org/paper/5afe92f561f01b43c644ca99e3c57926f25a5ac6
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In Applied Mathematics
In Computational Theory and Mathematics
In Control and Systems Engineering
Citations in the corpus
- Invariant measures of stochastic delay lattice systems (2021, background): “The random dynamics of stochastic lattice equations have been recently examined in [5, 6, 14, 15, 32, 33, 35, 61, 62] and the references therein.”
- Exponential Stability of Non-Autonomous Stochastic Delay Lattice Systems with Multiplicative Noise (2015, background): “The attractors of lattice equations have been investigated in [3,7,24,33,44] in the deterministic case, in [5,8,12,23,37,45] in the autonomous stochastic case, and in [6] in the non-autonomous stochastic case.”
- On differential equations with delay in Banach spaces and attractors for retarded lattice dynamical systems (2013, unknown): “, [6], [11], [12] [13], [26], [27], [35], [49], [46]).”