Dynamics of solutions of the Cauchy problem for semilinear parabolic stochastic partial differential equations with power-law singularities

Abstract

We prove a comparison theorem for bounded solutions of the Cauchy problem for stochastic partial differential equations of the parabolic type with linear leading part. The drift and diffusion coefficients have locally bounded derivatives with respect to the state variable. We use this comparison theorem to study the dynamics of solutions of an equation with an absorber and an equation with a source.