SPD

Abstract

Examples of linear and nonlinear parabolic equations in Hilbert spaces are given by the Kolmogorov equation and the Hamilton-Jacobi-Bellman equation related to SPDEs. In this talk we shall consider a class of semilinear parabolic equations in a Gauss-Sobolev space setting. By choosing a proper reference Gaussian measure, it will be shown that the existence and regularity of strong (variational) solutions can be proven in a similar fashion as parabolic equations in finite dimensions. The results are applied to two singular perturbation problems for parabolic equations containing a small parameter