# American Institute of Mathematical Sciences

2005, 2005(Special): 556-565. doi: 10.3934/proc.2005.2005.556

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

 1 University of Virginia, Department of Mathematics, Charlottesville, VA 22901, United States 2 Department of Mathematics, University of Virginia, P.O. Box 400137, Charlottesville, VA 22904

Received  September 2004 Revised  March 2005 Published  September 2005

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.
Citation: Irena Lasiecka, Roberto Triggiani. Global exact controllability of semilinear wave equations by a double compactness/uniqueness argument. Conference Publications, 2005, 2005 (Special) : 556-565. doi: 10.3934/proc.2005.2005.556
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