Exact controllability for semilinear wave equations
type: Item
instance of: scholarly article
title: Exact controllability for semilinear wave equations
zbMATH Open document ID: 0959.93029
author: Liangyu Li
author: Xu Zhang
published in: Journal of Mathematical Analysis and Applications
publication date: 2001-04-19T00:00:00Z
review text: The authors study the exact controllability of the system \[ {\partial^2 y(t, x) \over \partial t^2} - \Delta y(t, x) = f(y(t, x)) + \chi_\omega(x)u(t, x) \] in an \(n\)-dimensional domain \(\Omega\) with Dirichlet boundary condition, where \(\chi_\omega(x)\) is the characteristic function of a subdomain \(\omega \subseteq \Omega.\) Available results require linear growth of the nonlinearity \(f,\) except in space dimension \(n = 1.\) The author shows that for general \(n\) the system is exactly controllable under the superlinear growth condition \(f(s) = o(|s|\sqrt{\ln |s|})\) as \(s \to \infty.\)
Mathematics Subject Classification ID: 93C20
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 93C10
zbMATH DE Number: 1542466
zbMATH Keywords: exact controllability
zbMATH Keywords: semilinear control systems
zbMATH Keywords: hyperbolic control systems
reviewed by: Hector O. Fattorini
MaRDI profile type: Publication
full work available at URL: jmaa.2000.6998
OpenAlex ID: W2076965931
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DOI: 10.1006/JMAA.2000.6998
description: scientific article; zbMATH DE number 1542466