Global existence of mild solutions to non-autonomous stochastic evolution equations

Abstract We investigate the global existence of mild solutions for Cauchy problem to a class of non-autonomous stochastic evolution equations with additive noise, where the operators in linear part depend on time t and generate compact evolution family. Finally, we provide an illustrative example of practical significance to show the practical usefulness of the theoretical results that are obtained in this paper. The results obtained in this paper are supplement to the existing literature and essentially extend some existing results in this area. Mathematics Subject Classification (2010): 37B55; 37L55; 47J35; 60H15