Energy Decay and Boundary Control for Distributed Parameter Systems withViscoelastic Damping

摘要

This report concerns several aspects of damping and control in distributedparameter systems, with emphasis on applications to elastic and viscoelastic structures. For viscoelastic bodies, the ineffectiveness of boundary feedback for damping nonoscillatory 'creep' decay was demonstrated, and a precise energy space formulation was developed for the viscoelastic wave equation. In addition, a reachability result was proved for a second-order linear integral equation. For elastic beams and plates, exact controllability and the exponential decay of energy were established in new settings. These include uniform exponential decay of energy by means of locally distributed damping in a one-dimensional nonhomogeneous medium, and, under certain boundary conditions, for longitudinal vibrations in a thermoelastic rod.