Global exact controllability of semilinear wave equations by a double compactness/uniqueness argument

Pages: 556 - 565, Issue Special, August 2005

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Irena Lasiecka - University of Virginia, Department of Mathematics, Charlottesville, VA 22901, United States (email)
Roberto Triggiani - Department of Mathematics, University of Virginia, P.O. Box 400137, Charlottesville, VA 22904, United States (email)

Abstract: We prove exact controllability in the energy space of semilinear wave equations with $L_2$-Neumann boundary controls. The present proof integrates a double compactness/uniqueness PDE-based argument in establishing the uniform continuous observability inequality of the linearized, dual, uncontrolled problem with the abstract operator-theoretic approach proposed in [11], [21]. The latter approach analyzes suitable families of collectively compact operators [1] and ultimately culminates with the application of a global inversion theorem (homeomorphism) [4], [17] to the original controlled semilinear problem.

Keywords:  Semi-linear wave equations, exact boundary controllability.
Mathematics Subject Classification:  Primary: 35; Secondary: 93.

Received: September 2004;      Revised: March 2005;      Published: September 2005.