Volume 27, 2021
|Number of page(s)||32|
|Published online||19 March 2021|
Optimization of non-cylindrical domains for the exact null controllability of the 1D wave equation
Université Clermont Auvergne, Laboratoire de Mathématiques Blaise Pascal CNRS-UMR 6620,
Campus des Cézeaux,
Aubière cedex, France.
* Corresponding author: Arnaud.Munch@uca.fr
Accepted: 19 January 2021
This work is concerned with the null controllability of the one-dimensional wave equation over non-cylindrical distributed domains. The controllability in that case has been obtained by Castro et al. [SIAM J. Control Optim. 52 (2014)] for domains satisfying the usual geometric optic condition. We analyze the problem of optimizing the non-cylindrical support q of the control of minimal L2(q)-norm. In this respect, we prove a uniform observability inequality for a class of domains q satisfying the geometric optic condition. The proof based on the d’Alembert formula relies on arguments from graph theory. Numerical experiments are discussed and highlight the influence of the initial condition on the optimal domains.
Mathematics Subject Classification: 49Q10 / 93C20
Key words: Wave equation / Uniform observability / Optimal shape
© The authors. Published by EDP Sciences, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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