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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


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


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