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Controllability of Second-OrderEquations in

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  • Hugo Leiva
  • Nelson Merentes

Abstract

We present a simple proof of the interior approximate controllability for the following broad class of second-order equations in the Hilbert space : , , , , where is a domain in , , is an open nonempty subset of , denotes the characteristic function of the set , the distributed control belongs to and is an unbounded linear operator with the following spectral decomposition: , with the eigenvalues given by the following formula: , and is a fixed integer number, multiplicity is equal to the dimension of the corresponding eigenspace, and is a complete orthonormal set of eigenvectors (eigenfunctions) of . Specifically, we prove the following statement: if for an open nonempty set the restrictions of to are linearly independent functions on , then for all the system is approximately controllable on . As an application, we prove the controllability of the 1D wave equation.

Suggested Citation

  • Hugo Leiva & Nelson Merentes, 2010. "Controllability of Second-OrderEquations in," Mathematical Problems in Engineering, Hindawi, vol. 2010, pages 1-11, December.
    • Handle: RePEc:hin:jnlmpe:147195
    DOI: 10.1155/2010/147195
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