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].
@article{JEDP_2009____A2_0, author = {Ervedoza, Sylvain}, title = {Resolvent estimates in controllability theory and applications to the discrete wave equation}, journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles}, eid = {2}, pages = {1--18}, publisher = {Groupement de recherche 2434 du CNRS}, year = {2009}, doi = {10.5802/jedp.55}, language = {en}, url = {http://www.numdam.org/articles/10.5802/jedp.55/} }
TY - JOUR AU - Ervedoza, Sylvain TI - Resolvent estimates in controllability theory and applications to the discrete wave equation JO - Journées équations aux dérivées partielles PY - 2009 SP - 1 EP - 18 PB - Groupement de recherche 2434 du CNRS UR - http://www.numdam.org/articles/10.5802/jedp.55/ DO - 10.5802/jedp.55 LA - en ID - JEDP_2009____A2_0 ER -
%0 Journal Article %A Ervedoza, Sylvain %T Resolvent estimates in controllability theory and applications to the discrete wave equation %J Journées équations aux dérivées partielles %D 2009 %P 1-18 %I Groupement de recherche 2434 du CNRS %U http://www.numdam.org/articles/10.5802/jedp.55/ %R 10.5802/jedp.55 %G en %F JEDP_2009____A2_0
Ervedoza, Sylvain. Resolvent estimates in controllability theory and applications to the discrete wave equation. Journées équations aux dérivées partielles (2009), article no. 2, 18 p. doi : 10.5802/jedp.55. http://www.numdam.org/articles/10.5802/jedp.55/
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