Uniform large deviation principles of fractional reaction–diffusion equations driven by superlinear multiplicative noise on ℝn

In this paper, we investigate the uniform large deviation principle of the fractional stochastic reaction–diffusion equation on the entire space [Formula: see text] as the noise intensity approaches zero. The nonlinear drift term is dissipative and has a polynomial growth of any order. The nonlinear diffusion term is locally Lipschitz continuous and has a superlinear growth rate. By the weak convergence method, we establish the Freidlin–Wentzell uniform large deviations over bounded initial data as well as the Dembo–Zeitouni uniform large deviations over compact initial data. The main difficulties are caused by the superlinear growth of noise coefficients and the non-compactness of Sobolev embeddings on unbounded domains. The dissipativeness of the drift term and the idea of uniform tail-ends estimates of solutions are employed to circumvent these difficulties.