热–板传输系统的稳定性分析

In this paper, we study the stability of a coupled system which consists of a plate equation and a heat equation in adjacent domains, where the coupling comes from the transmission boundary conditions at the interface of the two domains. The heat equation is considered as the controller of the whole system. The dissipative damping produced in the heat equation affects the plate equation via the boundary connections. It is known that the energy of this two-dimensional system decays exponentially when there is an additional dissipation in the boundary of the plate part^[1]. In this paper, we obtain the exponential stability of the system with dissipation only in heat equation with the help of the frequency domain method, theory of elliptic equations, etc. It is consistent with the stability properties of corresponding one-dimensional beam-heat interaction system. Finally, we also analyze several plate-heat interaction systems with different coupling conditions.