Longtime behavior of the weakly coupled Euler-Bernoulli plate system with structural damping

Abstract

In this paper, we study the longtime behavior of the weakly coupled Euler-Bernoulli plate system with one structural damping. The system consists of two plate equations coupled by zero order terms. First, we show that when the coupling coefficient function is a nonzero constant and the damping coefficient function is a positive constant, the optimal energy decay rate of the system is t−23. Then we consider the case that the coupling and damping coefficient functions have compact supports. By Carleman estimate and the frequency domain method, we show that the energy of the system decays logarithmically when the supports of the coupling and damping coefficient functions satisfy suitable assumptions.