2022
DOI: 10.1016/j.jde.2022.07.026
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Existence, exponential mixing and convergence of periodic measures of fractional stochastic delay reaction-diffusion equations on Rn

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Cited by 23 publications
(5 citation statements)
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“…And then by the compactness method and the Prokhorov theorem, we obtain the existence of invariant measures (see Theorem 4.2). In addition, if f is periodic in t, we further show such an invariant measure is also periodic, which is different from [15,18,29,32] where the periodic measures do not have invariant property. For the existence of invariant measures of autonomous systems, we refer the reader to [13,46] for stochastic lattice systems and [6,14,30,37,52] for stochastic partial differential equations.…”
Section: Introductioncontrasting
confidence: 57%
“…And then by the compactness method and the Prokhorov theorem, we obtain the existence of invariant measures (see Theorem 4.2). In addition, if f is periodic in t, we further show such an invariant measure is also periodic, which is different from [15,18,29,32] where the periodic measures do not have invariant property. For the existence of invariant measures of autonomous systems, we refer the reader to [13,46] for stochastic lattice systems and [6,14,30,37,52] for stochastic partial differential equations.…”
Section: Introductioncontrasting
confidence: 57%
“…They provide a powerful framework for understanding and predicting the behavior of complex systems with memory, randomness, and time delays. See, for example, [1][2][3][4][5][6] and the references cited therein.…”
Section: Introductionmentioning
confidence: 99%
“…On the other hand, the theory of delayed partial differential equations has a wide range of physical background and practical mathematical models. In the last decade, fractional evolution equations with delay have also been investigated extensively, and some interesting results have been obtained (see [6,11,18,20]).…”
Section: Introductionmentioning
confidence: 99%