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2005, Volume 2005: 556-565. Doi: 10.3934/proc.2005.2005.556 open access
This issue Previous Article Properties of kernels and eigenvalues for three point boundary value problems Next Article Monotone local semiflows with saddle-point dynamics and applications to semilinear diffusion equations

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

  • 1.

    University of Virginia, Department of Mathematics, Charlottesville, VA 22901

  • 2.

    Department of Mathematics, University of Virginia, P.O. Box 400137, Charlottesville, VA 22904

Received:  August 31, 2004
Revised:  February 28, 2005
Published:  August 2005
Abstract Related Papers Cited by
    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.
    Mathematics Subject Classification: Primary: 35; Secondary: 93.

    Citation:
    shu

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