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This work is concerned with the distributed controllability of theone-dimensional wave equation over non-cylindrical domains. The controllabilityin that case has been obtained in [Castro-Cindea-Munch, Controllability of thelinear one-dimensional wave equation with inner moving forces, SIAM J. ControlOptim 2014] for domains satisfying the usual geometric optics condition. In thepresent work, we first show that the corresponding observability property holdstrue uniformly in a precise class of non-cylindrical domains. Within thisclass, we then consider, for a given initial datum, the problem of theoptimization of the control support and prove its well-posedness. Numericalexperiments are then discussed and highlight the influence of the initialcondition on the optimal domain.

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