Well-posedness and large deviations of fractional McKean-Vlasov stochastic reaction-diffusion equations on unbounded domains
arxiv(2024)
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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