Hostname: page-component-669899f699-rg895 Total loading time: 0 Render date: 2025-04-26T11:59:25.586Z Has data issue: false hasContentIssue false
  • English
  • Français

Stochastic systems governed by B-evolutions on Hilbert spaces

Published online by Cambridge University Press:  14 November 2011

N. U. Ahmed  and
S. Kerbal
N. U. Ahmed
Affiliation:
Department of Mathematics and Department of Electrical Engineering, University of Ottawa, 161 rue Louis-Pasteur, CP, Ottawa, Ontario, Canada K1N 6N5
S. Kerbal
Affiliation:
Department of Mathematics and Department of Electrical Engineering, University of Ottawa, 161 rue Louis-Pasteur, CP, Ottawa, Ontario, Canada K1N 6N5
Get access Rights & Permissions [Opens in a new window]

Synopsis

In this paper, we consider the question of existence of solutions and their regularity properties for a large class of stochastic evolution equations governed by B-evolutions involving two different Hilbert spaces. This allows dynamic boundary conditions together with noisy boundary data. They cover also stochastic boundary value problems. Our results are illustrated by two practical examples.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 127 , Issue 5 , 1997 , pp. 903 - 920
Copyright
Copyright © Royal Society of Edinburgh 1997

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1Ahmed, N. U.. Stochastic initial-boundary value problems for a class of second order evolution equations. In Proceedings of the International Conference on Theory and Applications of Differential Equations, Ohio University, 1 (1988), 13–19 (Columbus, Ohio: Ohio Univ. Press, 1988).Google Scholar
2Ahmed, N. U.. Relaxed controls for stochastic boundary value problems in infinite dimension. Proceeding IFIP WG 7.2 International Conference, Irse (1990), 1–10. Lecture Notes in Control and Information Sciences 149 (Irse, Germany: Springer Verlag, 1990).Google Scholar
3Ahmed, N. U.. Semigroup Theory with Applications to Systems and Control, Pitman Research Notes in Mathematics 246 (Harlow: Longman Scientific and Technical; and New York/London: John Wiley, 1991).Google Scholar
4Brill, H.. A semilinear evolution equation in a Banach space. J. Differential Equations 24 (1977), 41–225.CrossRefGoogle Scholar
5Prato, G. Da and Zabczyk, J.. Stochastic Equations In Infinite Dimensions, Encyclopedia of Mathematics and its Applications 44 (Cambridge: Cambridge University Press, 1992).CrossRefGoogle Scholar
6Dalsen, M. van. Die Teorie van Nie-stasionere Evolusies geassosieer met Dinamies-Gekoppelde Randwaardeprobleme (Doctoral Thesis, Pretoria University, 1978).Google Scholar
7Dalsen, M. van. Evolution problems involving non-stationary operators between two Banachspaces I. Existence and uniqueness theorems. Quaestiones Math. 8(2) (1985), 97–129.CrossRefGoogle Scholar
8Dalsen, M. van. Semilinear evolution equations and fractional powers of a closed pair ofoperators. Proc. Roy. Soc. Edinburgh Sect. A 105 (1987), 101–15.CrossRefGoogle Scholar
9Favini, A.. Laplace transform method for a class of degenerate evolution problems. Rend. Mat. Appl. 12 (1979), 511–36.Google Scholar
10Li, P., Lim, S. S., Vukovich, G. and Ahmed, N. U.. Stability and robustness analysis of boundary control of flexible space structure. Interna t. J.Systems Sci. 26 (1995), 1759–76.CrossRefGoogle Scholar
11Sauer, N.. Linear evolution equations in two Banach spaces. Proc. Roy. Soc. Edinburgh Sect. A 91 (1982), 287–303.CrossRefGoogle Scholar
12Sauer, N.. Dynamical processes associated with dynamic boundary conditions for partial differential equations. In Proceedings of the International Conference Theory and Applications of Differential Equations, Ohio University, 2 (1988), 374–8 (Columbus, Ohio: Ohio Univ. Press, 1988).Google Scholar