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arXiv · 2406.10694

Well-posedness and large deviations of fractional McKean-Vlasov stochastic reaction-diffusion equations on unbounded domains

Zhang Chen·Bixiang Wang
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Abstract

This paper is mainly concerned with the large deviation principle of the fractional McKean-Vlasov stochastic reaction-diffusion equation defined on R^n with polynomial drift of any degree. We first prove the well-posedness of the underlying equation under a dissipative condition, and then show the strong convergence of solutions of the corresponding controlled equation with respect to the weak topology of controls, by employing the idea of uniform tail-ends estimates of solutions in order to circumvent the non-compactness of Sobolev embeddings on unbounded domains. We finally establish the large deviation principle of the fractional McKean-Vlasov equation by the weak convergence method without assuming the time Holder continuity of the non-autonomous diffusion coefficients.

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Zhang Chen, Bixiang Wang. 2024-06-15. Well-posedness and large deviations of fractional McKean-Vlasov stochastic reaction-diffusion equations on unbounded domains. https://doi.org/10.1007/s00245-026-10426-y

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