The present article is a brief summary of the paper [27], which established new Carleman and observability estimates for a general class of linear wave equations. The main features of these estimates are that (a) they apply to a fully general class of time-dependent domains, with timelike moving boundaries, (b) they apply to linear wave equations in any spatial dimension and with general time-dependent lower-order coefficients, and (c) they allow for smaller time-dependent observation regions than previously obtained from existing Carleman estimate methods. In particular, the results of [27] imply exact controllability for general linear waves, again in settings of time-dependent domains and regions of control.
@article{SLSEDP_2018-2019____A11_0,
author = {Shao, Arick},
title = {On controllability of waves and {geometric~Carleman~estimates}},
journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications},
note = {talk:11},
pages = {1--14},
publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
year = {2018-2019},
doi = {10.5802/slsedp.134},
language = {en},
url = {http://www.numdam.org/articles/10.5802/slsedp.134/}
}
TY - JOUR AU - Shao, Arick TI - On controllability of waves and geometric Carleman estimates JO - Séminaire Laurent Schwartz — EDP et applications N1 - talk:11 PY - 2018-2019 SP - 1 EP - 14 PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique UR - http://www.numdam.org/articles/10.5802/slsedp.134/ DO - 10.5802/slsedp.134 LA - en ID - SLSEDP_2018-2019____A11_0 ER -
%0 Journal Article %A Shao, Arick %T On controllability of waves and geometric Carleman estimates %J Séminaire Laurent Schwartz — EDP et applications %Z talk:11 %D 2018-2019 %P 1-14 %I Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique %U http://www.numdam.org/articles/10.5802/slsedp.134/ %R 10.5802/slsedp.134 %G en %F SLSEDP_2018-2019____A11_0
Shao, Arick. On controllability of waves and geometric Carleman estimates. Séminaire Laurent Schwartz — EDP et applications (2018-2019), Exposé no. 11, 14 p. doi : 10.5802/slsedp.134. http://www.numdam.org/articles/10.5802/slsedp.134/
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