Xitence Of The Global Solution For P-system With Time-dependent Damping And Study Of Large Time Behavior

In this paper,we mainly consider the p-system with time-dependent damping,This model can be used to describe the damped Euler equations in the Largrange coordinates and acted as a model of compressible fluid through porous media,which has much physical meaning.In this paper the damping term indicates that the fric-tion will gradually disappear with time increasing.The work mainly consists of two aspects.Firstly,by using the characteristic line method and maximum principle,the existence of the integral smooth solution to Cauchy problem of p-system with dependent-time damping is proved.Then,by the energy method,we have obtained the Lp(2 ? p??)convergence rates and proved that the solution of p-system converges to that of the corresponding equation in the equilibrium state.Our results reduce the assumptions about the initial value of this problem and generalize the nonlinear stability results of the model.This article is arranged as follows:· In Chapter One,mainly introduces the research status of p-system of and summarizes the content arrangement and preparation knowledge of this paper.· In Chapter Two,it is proved existence of the global smooth solution of p-system with time-dependent damping.· In Chapter Three,it is proved large time behavior of p-system with time-dependent damping and Lp(2?p ??)convergence rate.