Bilinear Control for Global Controllability of the Parabolic-Elliptic Equations

In the present paper we establish the global approximate controllability of the parabolic-elliptic equations,which are governed in a bounded domain by a pair of controls:the traditional internal either locally distributed or lumped control; the lumped control entering the system as a time-dependent coefficient. The motivation for the latter is due to the well-known lack of global controllability properties for this kind of the pdepsilas when they are steered solely by former controls. Our approach involves an asymptotic technique allowing us to rdquoseparate and combinerdquo the impacts generated by the above-mentioned two types of controls. In particular, the addition of bilinear control allows us to reduce the use of the additive one to the local controllability technique only.