Stability Of A Transmission System Of Beam Equation And Heat Equation With Memory

In recent years,analysis about the coupling systems became one of the focus in the field of distributed parameter system.The interaction systems consist of two or several subsystems coupled through the interface.The properties of this system depend on the subsystems,the coupling conditions on the interface,the material near the interface,etc In this paper,we consider two kinds of boundary conditions of a transmission system including a beam equation and a heat equation with memory.By using the theory of C0 semigroup,partial differential equations,spectrum and frequency domain,we obtain that the energy of the system with two kinds of conditions decays exponentially when the relaxation function satisfies proper conditions.