## 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.

### MSC:

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

### Keywords:

exact controllability; hyperbolic systems