D. Comme, A) est dense dans 7l et que ,9(l) est un semi-groupe de contractions, il suffit de démontrer le résultat pour toute donnée initiale dans 2(A)

. Soit, D(A) D'après le Lemme (3.2), la trajectoire des solutions ((u,r,ri)(t))rro est bornée pour la norme du graphe. De plus, il est facile de voir que l'injêction i z D(A) --+ ?I est compacte et par conséquent la trajectoire est précompacte dans ?1

D. Le-principe-d-'inva,-riance-de-lasalle, on peut affirmer que l'ensembletr-limite @ (uo,uorqo) est un compact non vide invariant par le semigroupe S(t) et que de plus S(t) (u6, Th I.I2)

7. J. Ainsi-pour-tout-rn-)-|, llô{t)ll:"dt s c.llaollTw

F. L. Pour-prouver-ce-théorème,-on-utilise-le-théorème-de and . Huang, [18]) citê dans le chapitre I. Pour cela, on va estimer la résolvante sur l'axe imaginaire

?. La-condition and . Ir}-c-p, A) est déjà assurée par la stabilité forte. Il reste à prouver l'existence d'un réel M > 0 tel que ll

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