Exact and approximate controllability of abstract semilinear control systems
type: Item
instance of: scholarly article
title: Exact and approximate controllability of abstract semilinear control systems
zbMATH Open document ID: 1019.93003
author: Yanyan Li
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 2003-09-14T00:00:00Z
review text: The authors study exact and approximate controllability of an abstract semilinear control system of the form \[ \dot x(t)=Ax(t)+u(t)+f(t,x(t)), \quad 0\leq t\leq T, \qquad x(0)=x_{0}, \] where \(A: D(A)\subseteq V\to V\) is a closed linear operator with dense domain \(D(A)\) generating a \(C_{0}\)-semigroup, \(f: [0,T]\times V\to V\) a nonlinear operator which satisfies Carathéodory's conditions, \(u\in L^{2}([0,T],\hat{V})\) and \(V, \hat{V}\) Hilbert spaces.
reviewed by: Sotiris K. Ntouyas
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 93C25
Mathematics Subject Classification ID: 93C10
zbMATH DE Number: 1874467
zbMATH Keywords: controllability
zbMATH Keywords: semilinear control
zbMATH Keywords: Hilbert spaces
zbMATH Keywords: \(C_{0}\)-semigroup
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1874467