Invariant measures, periodic measures and pullback measure attractors of McKean-Vlasov stochastic reaction-diffusion equations on unbounded domains
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909327039660032 |
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| author | Shi, Lin Shen, Jun Lu, Kening Wang, Bixiang |
| author_facet | Shi, Lin Shen, Jun Lu, Kening Wang, Bixiang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_17548 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Invariant measures, periodic measures and pullback measure attractors of McKean-Vlasov stochastic reaction-diffusion equations on unbounded domains Shi, Lin Shen, Jun Lu, Kening Wang, Bixiang Probability Analysis of PDEs 60F10, 60H15, 37L55, 35R60 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. |
| title | Invariant measures, periodic measures and pullback measure attractors of McKean-Vlasov stochastic reaction-diffusion equations on unbounded domains |
| topic | Probability Analysis of PDEs 60F10, 60H15, 37L55, 35R60 |
| url | https://arxiv.org/abs/2409.17548 |