Controllability and stabilizability of vibrating simply supported plate with pointwise control (Q582968)

A necessary and sufficient condition for approximate controllability and, directly associated weak (and also strong) stabilizability of a problem- related evolutionary system is formulated. The main result states that even for a simple two-dimensional problem of elastic vibration, pointwise or finite-rank controllers may not provide controllability and stabilizability; exceptions are very sensitive to boundary conditions and regions. The case of a rectangular simply supported plate is discussed, where that sensitivity is mainly determined by the squared length-width- ratio.