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The Controllability of the Gurtin-Pipkin Equation: A Cosine Operator Approach

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An Erratum to this article was published on 20 September 2011

Abstract

In this paper we give a semigroup-based definition of the solution of the Gurtin-Pipkin equation with Dirichlet boundary conditions. It turns out that the dominant term of the input-to-state map is the control to displacement operator of the wave equation. This operator is surjective if the time interval is long enough. We use this observation in order to prove exact controllability in finite time of the Gurtin-Pipkin equation.

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Authors and Affiliations

  1. Politecnico di Torino, Dipartimento di Matematica, Corso Duca degli Abruzzi 24, 10129 Torino, Italy

    Luciano Pandolfi

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  1. Luciano Pandolfi
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Correspondence to Luciano Pandolfi.

Additional information

An erratum to this article is available at http://dx.doi.org/10.1007/s00245-011-9149-6.

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Pandolfi, L. The Controllability of the Gurtin-Pipkin Equation: A Cosine Operator Approach. Appl Math Optim 52, 143–165 (2005). https://doi.org/10.1007/s00245-005-0819-0

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  • DOI: https://doi.org/10.1007/s00245-005-0819-0

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