L~p-convergence Rates To Nonlinear Diffusive Waves For Solutions To Nonlinear Hyperbolic Conservation Laws With Damping

This paper is involved with the nonlinear hyperbolic conservation laws which describes the motion of isentropic gas flow with damping acting on it,such as a flow through porous media,the damped isentropic Euler equation is a perfect ex-ample,which has a lot of physical significance.In this paper we discuss the asymp-totic behavior for smooth solutions of isentropic Euler equation with damping.By some energy methods and careful analyze,we mainly obtain the global existence and LP(2≤p≤∞)convergence rates of classical solutions to this Cauchy prob-lem,whose solution converges to the solution of its corresponding porous media e-quation,and this new rates are much better than that obtained by predecessors.The paper is organized as follows:In Chapter One,we introduce the research background of nonlinear hyperbolic conservation laws,outline the content of the arrangement and prepare knowledge;In Chapter Two,we introduce the global existence and asymptotic behavior and Lp convergence rates of solutions to the nonlinear hyperbolic conservation laws.