Controllability to Rest for the “Plate Oscillation” Equation on the Torus in the Case of Local Force Action
Problems of local controllability for various systems with distributed parameters often arise in many applied problems, so this field is of significant interest. For classical systems of mechanics (membranes, thin plates), controllability problems are important in the cases where the control action is applied either to the boundary or to a part of the domain. This is due to the fact that, in practice, it is difficult to control the whole system, but it is possible to influence only a part of it. In this connection, the problem of choosing this part arises; for example, for the wave equation this choice is determined by the well-known geometric control condition (GCC). In our paper, no conditions are imposed on the subdomain affected by the control.