### SPDEs and parabolic equations in Gauss-Sobolev spaces

**Chow, P ***(Wayne State)*

Wednesday 26 May 2010, 09:45-10:45

Seminar Room 1, Newton Institute

#### 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

#### Presentation

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