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Journées équations aux dérivées partielles

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Sylvain Ervedoza
Resolvent estimates in controllability theory and applications to the discrete wave equation
Journées équations aux dérivées partielles (2009), Exp. No. 2, 18 p., doi: 10.5802/jedp.55
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Résumé - Abstract

We briefly present the difficulties arising when dealing with the controllability of the discrete wave equation, which are, roughly speaking, created by high-frequency spurious waves which do not travel. It is by now well-understood that such spurious waves can be dealt with by applying some convenient filtering technique. However, the scale of frequency in which we can guarantee that none of these non-traveling waves appears is still unknown in general. Though, using Hautus tests, which read the controllability of a given system in terms of resolvent estimates, we are able to prove that these spurious waves do not appear before some frequency scale. This document is based on the articles [12, 13, 14].

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