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March  2007, 18(2&3): 315-338. doi: 10.3934/dcds.2007.18.315

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

Igor Chueshov 1, and  Björn Schmalfuss 2,

1. 

Department of Mechanics and Mathematics, Kharkov National University, Kharkov, 61077, Ukraine
2. 

Mathematical Institute, University of Paderborn, Paderborn, 33098, Germany

Received  February 2006 Revised  September 2006 Published  March 2007

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.
Keywords: stochastic PDE, monotonicity., random dynamical systems, dynamical boundary conditions, pullback attractor.
Mathematics Subject Classification: primary: 37L55; secondary: 37H10, 37L30, 60H1.
Citation: Igor Chueshov, Björn Schmalfuss. Qualitative behavior of a class of stochastic parabolic PDEs with dynamical boundary conditions. Discrete and Continuous Dynamical Systems, 2007, 18 (2&3) : 315-338. doi: 10.3934/dcds.2007.18.315
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