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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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