Displaying similar documents to “The Rothe's method to a parabolic integrodifferential equation with a nonclassical boundary conditions.”

On mild solutions of gradient systems in Hilbert spaces

Andrzej Rozkosz (2013)

Open Mathematics

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We consider the Cauchy problem for an infinite-dimensional Ornstein-Uhlenbeck equation perturbed by gradient of a potential. We prove some results on existence and uniqueness of mild solutions of the problem. We also provide stochastic representation of mild solutions in terms of linear backward stochastic differential equations determined by the Ornstein-Uhlenbeck operator and the potential.