The Large Time Asymptotic Behavior And Convergence Rate Of Solutions Of The Non-isentropic P-equations With Time-dependent Damping

We study the large time asymptotic behavior and the existence of solutions Cauchy problem of the non-isentropic p-system with time-dependent damping.The motion model of the compressible flow can be described by the non-isentropic p-system with time-dependent damping,which has rich physical significance.The Damping of the system(?)for 0<?<1,where damping effect is time-gradually-degenerate.We use the energy methods and the weighted estimation to prove the large time asymptotic behavior,the existence and convergence rate for solutions Cauchy problem of the non-isentropic p-system with time-dependent damping.We generalize the results in Pan[16,26]to the the non-isentropic p-system with constant damping.The paper is organized as follows:In Chapter One,we introduce the research background of the problem for non-isentropic p-system with time-dependent damping,outline the content of the ar-rangement and prepare knowledge.In Chapter Two,the existence and decay estimate of the nonlinear diffusive waves are studied.In Chapter Three,we study the large time asymptotic behavior and convergence rate of solutions of the non-isentropic p-equations.