On the controllability problem with pointwise observation for the parabolic equation with free convection term

摘要

A mathematical model of the temperature control in industrial greenhouse is based on a one-dimensional parabolic equation with a free convection term and a quadratic cost functional with the point observation. The existence and uniqueness of a control function from some convex set of functions are proved and the structure of the set of accessible temperature functions is studied. We also prove the dense controllability of the problem for some set of control functions.