Uniform observability of the one-dimensional wave equation for non-cylindrical domains. Application to the control's support optimization
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.
Keywords
Cite
@article{arxiv.1911.01284,
title = {Uniform observability of the one-dimensional wave equation for non-cylindrical domains. Application to the control's support optimization},
author = {Arthur Bottois and Nicolae Cindea and Arnaud Munch},
journal= {arXiv preprint arXiv:1911.01284},
year = {2019}
}