Controllability of some bilinear and semilinear parabolic problems

We present in this paper a survey of recent results on the controllability of the parabolic system governed by bilinear control. We first discuss the problem of global controllability which corresponds to the question of whether the solution of the system can be driven to a given state at a some finite time by means of a control. We give some results on the global controllability of bilinear and semilinear reaction-diffusion equations. After this we introduce the case of partial controllability with the control acting on a subregion of the domain. Illustrative examples are also provided.

Global blowup controllability of heat equation with feedback control

This paper concerns a global controllability problem for heat equations. In the absence of control, the solution to the linear heat system globally exists. While for each initial data, we can find a feedback control acting on an internal subset of the space domain such that the corresponding solution to the system blows up at given time.