Equations d'etat bien posees en controle bilineaire (Well-posed state equations in bilinear control) (Q2891111)

The author considers the following abstract bilinear control problem NEWLINE\[NEWLINE\dot{z}(t)+A(t,z(t))=B(t,u(t),z(t))+f(t)\text{ a.a. }t\in [0,T],\, z(0)=z^0,NEWLINE\]NEWLINE where \(u\) is the control and \(f\) is the perturbation, \(A\) is a nonlinear operator and \(B\) is a bilinear operator with respect to the control and the state of the type \(B(u,z)=u\cdot z\). The author proves that the problem is well-posed in the sense of Hadamard and that there is an unique solution to it which continuously depends on \(z^0\), \(u\) and \(f\).