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Invariant measures, periodic measures and pullback measure attractors of McKean-Vlasov stochastic reaction-diffusion equations on unbounded domains

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arxiv 2409.17548 v1 pith:66XR3YJH submitted 2024-09-26 math.PR math.AP

Lin Shi , Jun Shen , Kening Lu , Bixiang Wang This is my paper · ORCID
classification math.PRmath.AP
keywords measuresattractorsequationsinvariantmeasureperiodicpullbackstochastic
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This paper deals with the long term dynamics of the non-autonomous McKean-Vlasov stochastic reaction-diffusion equations on R^n. We first prove the existence and uniqueness of pullback measure attractors of the non-autonomous dynamical system generated by the solution operators defined in the space of probability measures. We then prove the existence and uniqueness of invariant measures and periodic measures of the equation under further conditions. We finally establish the upper semi-continuity of pullback measure attractors as well as the convergence of invariant measures and periodic measures when the distribution dependent stochastic equations converge to a distribution independent system.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Uniform measure attractors of McKean-Vlasov stochastic reaction-diffusion equations on unbounded thin domain

    math.PR 2024-12 conditional novelty 6.0 of 10

    Uniform measure attractors exist uniquely for non-autonomous McKean-Vlasov stochastic reaction-diffusion equations on unbounded thin domains and converge to the attractor of the collapsed limit equation as the thickne...

  2. Pullback measure attractors and limiting behaviors of McKean-Vlasov stochastic delay lattice systems

    math.DS 2024-12 conditional novelty 5.0 of 10

    Pullback measure attractors exist uniquely for non-autonomous McKean-Vlasov stochastic delay lattice systems, are singleton and exponentially mixing under stronger damping, and are upper semicontinuous as distribution...

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