2019
DOI: 10.1515/math-2019-0099
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Random uniform exponential attractor for stochastic non-autonomous reaction-diffusion equation with multiplicative noise in ℝ3

Abstract: We first introduce the concept of the random uniform exponential attractor for a jointly continuous non-autonomous random dynamical system (NRDS) and give a theorem on the existence of the random uniform exponential attractor for a jointly continuous NRDS. Then we study the existence of the random uniform exponential attractor for reaction-diffusion equation with quasi-periodic external force and multiplicative noise in ℝ3.

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“…Finally, we note that in Han and Zhou (2019) recently constructed a random uniform exponential attractor for a stochastic reaction-diffusion equation with quasi-periodic forcings. Their result was derived by taking into account an extended phase space and then studying its respective skew-product semiflow, for which the problem is then reduced to an autonomous problem.…”
Section: Introductionmentioning
confidence: 97%
“…Finally, we note that in Han and Zhou (2019) recently constructed a random uniform exponential attractor for a stochastic reaction-diffusion equation with quasi-periodic forcings. Their result was derived by taking into account an extended phase space and then studying its respective skew-product semiflow, for which the problem is then reduced to an autonomous problem.…”
Section: Introductionmentioning
confidence: 97%