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Qualitative behavior of a class of stochastic parabolic PDEs with dynamical boundary conditions

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  • We consider non-linear parabolic stochastic partial differential equations with dynamical boundary conditions and with a noise which acts in the domain but also on the boundary and is presented by the temporal generalized derivative of an infinite dimensional Wiener process. We prove that solutions to this stochastic partial differential equation generate a random dynamical system. Under additional conditions we show that this system is monotone. Our main result states the existence of a compact global (pullback) attractor.
    Mathematics Subject Classification: primary: 37L55; secondary: 37H10, 37L30, 60H15.

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