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Well-posedness and large deviations of fractional McKean-Vlasov stochastic reaction-diffusion equations on unbounded domains
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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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Cited by 1 Pith paper
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Uniform Large Deviations of Mckean-Vlasov Stochastic Fractional $(\alpha,p)$-Laplacian Equations Driven by Superlinear Noise on $\mathbb{R}^d$
McKean–Vlasov stochastic fractional (α,p)-Laplacian equations with superlinear multiplicative noise on R^d are globally well-posed and satisfy Freidlin–Wentzell and Dembo–Zeitouni uniform large deviation principles.
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