Controllability of semilinear stochastic systems in Hilbert spaces.
type: Item
instance of: scholarly article
title: Controllability of semilinear stochastic systems in Hilbert spaces.
zbMATH Open document ID: 1109.93305
DOI: 10.1016/S0022-247X(03)00592-4
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-01-26T00:00:00Z
review text: The author studies weak approximate and complete controllability of the following semilinear stochastic system \[ \begin{gathered} dx(t)= [Ax(t)+ Bu(t)+ F(t,x(t),u(t))]\,dt+ \Sigma(t,x(t),u(t))dw(t),\\ x(0)= x_0,\quad t\in[0,T].\end{gathered}\tag{1} \] where \(A: H\to H\) is an infinitesimal generator of strongly continuous semigroup \(S(\cdot)\), \(B\in L(0,H)\), \(F: [0,T]\times H\times U\to H\), \(\Sigma: [0,T]\times H\times U\to L^0_2\); \(H, U\) are Hilbert spaces and \(w\) is a suitably chosen Wiener process. To this end the author introduces the weak approximate controllability concept for stochastic systems which is a weaker concept than the usual ones, that is, approximate controllability and complete controllability. The author presents sufficient conditions for weak approximate and complete controllability of (1) and provides the paper with several examples.
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 93E03
zbMATH DE Number: 2032583
zbMATH Keywords: weak approximate controllability
zbMATH Keywords: complete controllability
zbMATH Keywords: stochastic differential equation
author: Nazim Idrisoglu Mahmudov
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2032583