Contrôlabilité exacte pour des domaines minces. (Exact controllability for thin domains). (French) Zbl 0795.93016

This note studies the exact controllability of hyperbolic systems on a thin domain \(\Omega\times (0,\varepsilon)\subset\mathbb{R}^{n+1}\) using an optimal control approach due to J. L. Lions. This method gives rise to an operator \(\Lambda_ \varepsilon\) mapping the initial values of an associated boundary value problem (without controls) to the ‘final’ values of a dual problem in reverse time. However, as \(\varepsilon\to 0\), the operators \(\Lambda_ \varepsilon\) do not tend to the corresponding operator \(\Lambda\) for the \(n\)-dimensional domain \(\Omega\). The author introduces a modification of the operators so as to obtain the desired limit behaviour. Unfortunately the note is not easily readable: It consists of a sequence of 86 formulae with a minimum of interconnecting text in between.


93B05 Controllability
93C20 Control/observation systems governed by partial differential equations