The Cauchy Problem For The Plate Equations With The Weak Damped Term

This paper consists of four chapters.The first chapter is the introduction which will give the physical meaning and research results of the equation. In the second chapter, we will give the notations and inequalities. In the third chapter,we will study the large time behavior of solutions to the cauchy problem for the generalized plate equations with the weak damped termFirst of all,applying the Duhamel principle,the cauchy problem for the linearized plate equation is written an equivalence integral equation. Furthermore we establish the decay estimate and existence of the solution to the linearized plate equation. Then using the contraction mapping principle and integral estimates we give the existence and uniform decays to the cauchy problem of the generalized plate equation in the case that the initial data are small.