Well-Posedness for Nonlinear Parabolic Stochastic Differential Equations with Nonlinear Robin Conditions

In this paper, we present the existence and uniqueness of strong probabilistic solutions for nonlinear parabolic Stochastic Partial Differential Equations (SPDEs) with Robin boundary conditions in a domain holes. On holes, condition is imposed, while homogeneous Dirichlet prescribed on exterior boundary. The coefficient matrix assumed to be symmetric, random forces are satisfy some types regularities. We use Galerkin’s approximation method, compactness results from stochastic calculus.