Energy Decay Of Coupled Wave Equations In Exterior Domain

Partial differential equation(PDE)is an important branch of modern mathematics.Wave equations are classical and important PDEs,which are from real life and of extensive applications in the physics and engineering fields.The energy decay of two kinds of coupled wave equations in exterior domain are studied in the thesis.The thesis consists of three chapters.In Chapter 1,we provide a simple summary of the research state and background for the energy decay of wave equations in exterior domain.The main research problems of this thesis are introduced briefly.In Chapter 2,the wave equations coupled by displacements is studied(?)Where ? is the exterior domain of a compact domain;T is the boundary of ?.a(·)>0 is the coefficient function of the damping and ?(·)>0 is the coupled function.The local energy decay of the system is studied in this chapter.Assume that two wave systems are coupled in a neighborhood of the boundary and the damping of the system is only applied in a bounded region.By using the multiplier method,the weighted function method and the truncation technique,we prove the polynomial decay estimation of the local energy decay of the coupled system.In Chapter 3,the energy decay of the wave equations coupled by velocities is studied(?)Where ? is the exterior domain of a compact domain;? is the boundary of ?.The local energy decay of the system is proved by using the multiplier method,the weighted function method and the truncation technique under some assumptions similar to those in Chapter 2.