## Study of a non-classical perturbed optimal control system. (Étude d’un système de contrôle optimal perturbé non classique.)(French)Zbl 0899.49002

The paper deals with a perturbed optimal control problem arising in aerodynamics. The state equation is $\begin{cases} -\Delta y_\varepsilon(v)=0 & \text{in $$\Omega$$;}\\ \partial y_\varepsilon(v)\over\partial\nu+\varepsilon y_\varepsilon(v)=0 & \text{on\;$$\Gamma$$},\qquad\qquad y_\varepsilon(v)\in H^1(\Omega),\end{cases}$ where $$\Gamma=\partial\Omega$$ is smooth, and $$\Omega$$ locally lies on one side of $$\Gamma$$. Denoting by $$T_\varepsilon:L^2(\Gamma)\to L^2(\Gamma)$$ the map $$v\mapsto {y_\varepsilon(v)}_\Gamma$$, the cost functional is $$J_\varepsilon(v)=\| T_\varepsilon(v)-z\|^2_2$$, with $$z$$ a given non zero vector in $$L^2(\Gamma)$$, and $$v$$ varies in some subspace of admissible controls. The paper deals with existence and uniqueness of optimal controls $$v_\varepsilon$$, and with their behaviour as $$\varepsilon\to 0$$.
Reviewer: L.Ambrosio (Pavia)

### MSC:

 49J20 Existence theories for optimal control problems involving partial differential equations 93C73 Perturbations in control/observation systems
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### References:

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