论文信息 - A Semigroup Approach to Stochastic Dynamical Boundary Value Problems

A Semigroup Approach to Stochastic Dynamical Boundary Value Problems

In many physical applications, the evolution of the system is endowed with dynamical boundary conditions, i.e., with boundary operators containing time derivatives. In this paper we discuss a generalization of such systems, where stochastic perturbations affect the way the system evolves in the interior of the domain as well as on the boundary.

Stefano Bonaccorsi | G. Ziglio | S. Bonaccorsi | G. Ziglio

[1] J. Zabczyk,et al. Evolution equations with white-noise boundary conditions , 1993 .

[2] Marco Fuhrman,et al. Optimal control of a stochastic heat equation with boundary-noise and boundary-control , 2007 .

[3] H. Beckert,et al. J. L. Lions and E. Magenes, Non‐Homogeneous Boundary Value Problems and Applications, II. (Die Grundlehren d. Math. Wissenschaften, Bd. 182). XI + 242 S. Berlin/Heidelberg/New York 1972. Springer‐Verlag. Preis geb. DM 58,— , 1973 .

[4] G. Nickel,et al. Dynamic Boundary Conditions and Boundary Control for the One-Dimensional Heat Equation , 2004 .

[5] Igor Chueshov,et al. Parabolic stochastic partial differential equations with dynamical boundary conditions , 2004, Differential and Integral Equations.

[6] J. Lions,et al. Non-homogeneous boundary value problems and applications , 1972 .

[7] Jerzy Zabczyk,et al. Ergodicity for Infinite Dimensional Systems: Appendices , 1996 .

[8] Tyrone E. Duncan,et al. Ergodic Boundary/Point Control of Stochastic Semilinear Systems , 1998 .

[9] Rainer Nagel,et al. A Semigroup Approach to Boundary Feedback Systems , 2003 .

[10] R. Nagel. The spectrum of unbounded operator matrices with non-diagonal domain , 1990 .

[11] J. Zabczyk,et al. Stochastic Equations in Infinite Dimensions , 2008 .