Convergence Of Strongly Nonlinear Diffusion Waves For The Solution Of Euler Equation With Damping

The damped isentropic Euler equation is a kind of typical nonlinear hyperbol-ic conservation law equation,which describes the movement of compressible fluid through porous media and has rich physical significance.By using energy method and detailed analysis,we obtain the smooth solution of isentropic Euler equation converges to the solution of porous medium equation asymptotically.The initial value of this paper can be a certain large initial value,and there is no small condi-tion of prior hypothesis in the solution space.Unlike Zhao[19],we need to analyze and estimate the nonlinear convection term in the equation carefully.This article has the following plans:First of all,it describes the research basis,the theoretical knowledge needed and the main results of this paper.Secondly,the properties of the nonlinear diffusion wave and the proof process of the results in this paper are given.Finally,The convergence rate of L~p for the solution of the equation is derived.