Portugaliae Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 57, No. 4, pp. 493-508 (2000)

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Exact Distributed Controllability for The Semilinear Wave Equation

Wei-Jiu Liu

Department of Mathematics and Statistics, Dalhousie University,
Halifax, Nova Scotia, B3H3J5 - CANADA
E-mail: weiliu@mathstat.dal.ca

Abstract: In this paper we generalize the theorems of exact controllability for the linear wave equation with a distributed control to the semilinear case, showing that, given $T$ large enough, for every initial state in a sufficiently small neighbourhood of the origin in a certain function space, there exists a distributed control, supported on a part of a domain, driving the system to rest. Also, if the control is allowed to support on the entire domain, then we prove that the system is globally exactly controllable at any time $T$.

Keywords: Distributed controllability; semilinear wave equation.

Classification (MSC2000): 93B05, 35B37, 35L05.

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Electronic version published on: 31 Jan 2003. This page was last modified: 27 Nov 2007.

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