Study On The Stability Of Solutions Of Two Classes Of Coupled Systems Of Hyperbolic Partial Differential Equations

In this paper,we study the stability of solutions of two classes of coupled systems of hyperbolic partial differential equations.The existence and uniqueness of global solutions of the two systems will be analyzed respectively.We will prove that each system has a polynomial rate of decay as time tends to infinity with the method of higher order energy and a theorem by Gearhart,but is not exponentially stable.One class is wave-Plate coupled system Another class is the weakly coupled wave equations system with the term with memory only acting on one of the equations...