Abstract
We discuss the early results from [8] on global approximate reachability of the 1-D wave equation with Dirichlet boundary conditions and the rod equation with hinged ends in the case when the multiplicative control is time-dependent only. The methods of [8] make use of the inverse function theorem and involve dealing with the associated Riesz bases of exponential time-dependent functions under the additional assumption that all the modes in the initial datum are present.
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© 2010 Springer-Verlag Berlin Heidelberg
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Khapalov, A.Y. (2010). The 1-D Wave and Rod Equations Governed by Controls That Are Time-Dependent Only. In: Controllability of Partial Differential Equations Governed by Multiplicative Controls. Lecture Notes in Mathematics(), vol 1995. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12413-6_9
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DOI: https://doi.org/10.1007/978-3-642-12413-6_9
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-12412-9
Online ISBN: 978-3-642-12413-6
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