Contrôlabilité exacte et homogénéisation. I. (Exact controllability and homogenization. I). (French) Zbl 0659.49002

Lions, J.-L.

Asymptotic Anal. 1, No. 1, 3-11 (1988).

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)

Keywords:

evolution operators of hyperbolic type or of Petrowsky’s type; homogenization; exact controllability