Random attractors for stochastic semilinear degenerate parabolic equations with delay

Shangzhi Li and Shangjiang Guo

Physica A: Statistical Mechanics and its Applications, 2020, vol. 550, issue C

Abstract: In this paper, we consider a stochastic semilinear degenerate parabolic equation with delay in a bounded domain in RN and the nonlinearity satisfying an arbitrary polynomial growth condition. The random dynamical system generated by the equation is shown to have a random attractor in C([−τ,0],Lp(O)∩D01(O,σ)), which is a compact and invariant tempered set and attracts every tempered random subset of C([−τ,0],L2(O)) in the topology of C([−τ,0],Lp(O)). In a particular case, the random attractor consists of singleton sets (i.e., a random fixed point), which generates an exponentially stable non-trivial stationary solution. This theoretical result improves some recent ones for stochastic semilinear degenerate parabolic equations.

Keywords: Random dynamical system; Random attractor; Regularity; Stochastic degenerate parabolic equation; A priori estimate method (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:550:y:2020:i:c:s0378437120300170

DOI: 10.1016/j.physa.2020.124164

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