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.
Martingale Solutions of Fractional Stochastic Reaction-Diffusion Equations Driven by Superlinear Noise
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abstract
In this paper, we prove the existence of martingale solutions of a class of stochastic equations with pseudo-monotone drift of polynomial growth of arbitrary order and a continuous diffusion term with superlinear growth. Both the nonlinear drift and diffusion terms are not required to be locally Lipschitz continuous. We then apply the abstract result to establish the existence of martingale solutions of the fractional stochastic reaction-diffusion equation with polynomial drift driven by a superlinear noise. The pseudo-monotonicity techniques and the Skorokhod-Jakubowski representation theorem in a topological space are used to pass to the limit of a sequence of approximate solutions defined by the Galerkin method.
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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.