PERIODICALLY REACHABLE SETS OF NONLINEAR PARABOLIC SYSTEMS UNDER PERIODIC FORCING

We study periodicity and periodic controllability of solutions of nonlinear parabolic equations when periodic or asymtotically periodic control functions are given as boundary conditions. Introducing an inequality condition on the system parameters, the constant on the stability of the linear operator and the growth rate or the (local) Lipschitz constant of the nonlinear term, we show the asymptotically periodic stability and controllability of solutions