Large Deviation Principles of Fractional Stochastic Nonclassical Diffusion Equations on Unbounded Domains

ABSTRACT In this paper, we study the large deviation principle (LDP) of the fractional stochastic nonclassical diffusion equation with superlinear drift driven by nonlinear noise defined on unbounded domains. We first prove the well‐posedness and the strong convergence of solutions of the corresponding control equation with respect to control in the weak topology. We then prove the convergence in probability of solutions of the stochastic equation as the noise intensity approaches zero, and finally establish the LDP of the stochastic equation by the weak convergence method. The noncompactness of Sobolev embeddings on unbounded domains is overcome by the uniform tail‐ends estimates on the solutions of the control equation.