# zbMATH — the first resource for mathematics

Contrôlabilité exacte et homogénéisation. I. (Exact controllability and homogenization. I). (French) Zbl 0659.49002
The author presents a problem concerning an asymptotic behavior of evolution operators of hyperbolic type or of Petrowsky’s type, depending of a parameter $$\epsilon$$. The parameter $$\epsilon$$ is related with rapidly varying coefficients in the framework of homogenization theory.
The author studies for these operators the exact controllability problem. The main result is that the optimal control limit for the rapidly varying systems is the optimal control for the homogenized system.
Reviewer: M.Codegone

##### MSC:
 49J20 Existence theories for optimal control problems involving partial differential equations 35L10 Second-order hyperbolic equations 93B03 Attainable sets, reachability 49K20 Optimality conditions for problems involving partial differential equations 49J45 Methods involving semicontinuity and convergence; relaxation 93B05 Controllability 93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)