Controllability in a nonlinear parabolic problem with integral overdetermination (Q2387955)

The author considers the controllability in a nonlinear parabolic problem with integral over-determination. Some authors studied the controllability problem for the linear heat equation. However, actual heat diffusion processes cannot be described by a linear equation, and hence they introduce a very simple nonlinear term for which the problem remains uniquely solvable. Diffusion processes can not be described by more complicated nonlinearities, and so the present paper can be treated as one of the first steps in this direction.