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 controllability of the one-dimensional wave equation with controls distributed over non-cylindrical domains. The controllability in that case has been obtained in [Castro-Cîndea-Münch, 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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Submitted on : Monday, November 4, 2019 - 1:27:09 PM
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Arthur Bottois, Nicolae Cindea, Arnaud Munch. Uniform observability of the one-dimensional wave equation for non-cylindrical domains. Application to the control's support optimization. 2019. ⟨hal-02345036⟩

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