Large Time Behavior And Convergence Rates Of Solutions Of P-System With Time-Dependent Damping

P-system with time-dependent damping are a typical class of nonlinear hyperbolic conservation law equations,which describe the movement of compressible fluid through porous media and have rich physical significance.Using the energy method and careful analysis,we obtain the asymptotic state and convergence rate of the smooth solution of the time-damped P-system.The asymptotic state is an asymptotic expansion of the solution of the porous media equation.The convergence rate obtained is the same as Geng-Huang-Jin-Wu [5],but the initial value we require is a certain large initial value,and the solution has no minimality condition of prior assumption in the solution space.The paper is arranged as follows:In Chapter One,the research status of P-equations with time-dependent damping is introduced.The main results of this paper,the time asymptotic expansion of nonlinear diffusion waves and the theoretical knowledge needed are summarized.In Chapter Two,the existence of p-system solutions is proved and the attenuation estimates are obtained.In Chapter Three,we proves the lemma 1.3.3.