Un petit aperçu des questions d'existence globale, p.63 ,
,
, Nouveau résultat de contrôlabilité locale en temps petit avec trois contrôles, Étude approfondie du système de quatre espèces chimiques : nouveaux résultats de contrôlabilité
69 7.4.4 Nouveau résultat de contrôlabilité globale en temps long et en petite dimension ,
, Retour au cas général d'un système de taille arbitraire : nouveau résultat de contrôlabilité locale
73 7.6.2 Contrôlabilité locale du système de Keller-Segel à des états stationnaires non constants ,
,
Another interesting problem could be to determine if Theorem E.8.6 and Theorem E.8.10 can be generalized with fewer controls than equations in (E.173). The usual strategy of Luz de Teresa to ,
, optimal" (with a sense to precise) control for (E.20) (see for instance [FCM12, Section 2] or [FCM14]). A variational characterization of the control could be probably obtained as in [FCM14, Proposition 2.1] by using Stampacchia's theorem (see [Bre11, Theorem 5.6]) instead of Lax Milgram's theorem. Then, we could implement a numerical method to
, We deduce from (F.17) and (F
, T ? ) × ?) d 1 × C ? c ((T ? , T ) × ?) d 2 such that S(?; f 0 , u) ? F T . By the Hilbert Uniqueness Method, it is sufficient to prove an observability inequality for S(t) * . By using the finite-dimensionality of F ? T, We prove that any element of L 2 (T) d can be steered to F T in an arbitrary short time , i.e. for every ? > 0 and f 0 ? L 2 (T) d , there exists u ? L, vol.6
, Step 5 implies the controllability of the system in any time ? > T . As T is an arbitrary time
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