Optimal design of sensors for a damped wave equation

Yannick Privat (1) , Emmanuel Trélat (1)

1 LJLL - Laboratoire Jacques-Louis Lions

In this paper we model and solve the problem of shaping and placing in an optimal way sensors for a wave equation with constant damping in a bounded open connected subset Ω of IR n. Sensors are modeled by subdomains of Ω of a given measure L|Ω|, with 0 < L < 1. We prove that, if L is close enough to 1, then the optimal design problem has a unique solution, which is characterized by a finite number of low frequency modes. In particular the maximizing sequence built from spectral approximations is stationary.

Domaines: Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

Yannick Privat, Emmanuel Trélat. Optimal design of sensors for a damped wave equation. 10th AIMS Conference, Nov 2015, madrid, France. pp.936--944, ⟨10.3934/proc.2015.0936⟩. ⟨hal-01160306⟩