On the impossibility of bringing a flat membrane to rest with boundary forces

We consider exact control problems for the oscillations of two-dimensional membranes with boundary forces. We say that a system can be brought to the state of rest of for any initial conditions there exists a control such that the corresponding solution becomes zero in finite time and remains zero in the future. We prove that under certain restrictions on the controlling influence some systems with distributed parameters cannot be brought to the state of rest in finite time.