Backward regularity of attractors for lattice FitzHugh-Nagumo system with double random coefficients

Fuzhi Li and Dongmei Xu

Applied Mathematics and Computation, 2022, vol. 430, issue C

Abstract: In this paper, we investigate the backward compact dynamical behavior for the stochastic lattice FitzHugh-Nagumo system with double random coefficients and multiplicative noise. It is proved, under some suitable conditions on the nonlinear term and the body force, that the system has a unique backward compact bi-spatial random (ℓσ2×ℓσ2,ℓσp×ℓσ2)-attractor for any p>2. By such a bi-spatial attractor we mean an invariant backward compact set in ℓσp×ℓσ2 that pullback attracts all nonempty subsets of ℓσ2×ℓσ2 under another topology of ℓσp×ℓσ2. The time-dependent uniform pullback asymptotical compactness of the solution operators in ℓσp×ℓσ2 is proved by virtue of a cut-off technique and considering two different attracting universes to overcome several difficulties caused by the lack of compact Sobolev embeddings in the case of a lattice system and the unknown measurability of random attractor.

Keywords: Stochastic lattice system; Double random coefficients; Backward compactness; Regularity; Bi-spatial random attractor (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:430:y:2022:i:c:s0096300322003794

DOI: 10.1016/j.amc.2022.127305

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