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Domain decomposition for the control of systems governed by evolution equations. (Décomposition de domaine pour le contrôle de systèmes gouvernés par des équations d’évolution.) (French. Abridged English version) Zbl 0879.35090
Summary: We present a non-overlapping iterative domain decomposition method with “coupled” Robin transmission conditions. We prove its convergence on an optimal control problem for the wave equation. The linear part of the “feedback” law associated to the local optimal control problems set on subdomains is independent of the iterative process. The method can be applied, at least formally, to the optimal control of systems governed by evolution equations.

MSC:
35L20 Initial-boundary value problems for second-order hyperbolic equations
35A35 Theoretical approximation in context of PDEs
35L05 Wave equation
35B37 PDE in connection with control problems (MSC2000)
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