Energy Decay Rate of the Plate Equation with Potential and Indefinite Damping

摘要

We consider the plate equation with an indefinite sign damping and a zero order potential term. By means of the global Carleman-type estimate and the usual energy estimate, we show that the energy of the system decays exponentially. Also, using the classical perturbation theory, we give an explicit upper bound estimate on the negative damping to guarantee the exponential decay rate.