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arXiv · 1911.01284

Uniform observability of the one-dimensional wave equation for non-cylindrical domains. Application to the control's support optimization

Arthur Bottois·Nicolae Cindea·Arnaud Munch
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Abstract

This work is concerned with the distributed controllability of the one-dimensional wave equation over non-cylindrical domains. The controllability in that case has been obtained in [Castro-Cindea-Munch, Controllability of the linear one-dimensional wave equation with inner moving forces, SIAM J. Control Optim 2014] for domains satisfying the usual geometric optics condition. In the present work, we first show that the corresponding observability property holds true uniformly in a precise class of non-cylindrical domains. Within this class, we then consider, for a given initial datum, the problem of the optimization of the control support and prove its well-posedness. Numerical experiments are then discussed and highlight the influence of the initial condition on the optimal domain.

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Arthur Bottois, Nicolae Cindea, Arnaud Munch. 2019-11-04. Uniform observability of the one-dimensional wave equation for non-cylindrical domains. Application to the control's support optimization. https://arxiv.org/abs/1911.01284

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