The Existence Of Large Rarefaction Waves For The Piston Problem Of P-system

There is a uniform section of the elongated tube,it is placed horizontally,infinitely long and filled with static gas.There is a piston in the middle of the tube.When the piston moves to the left at a certain speed,it causes the movement of the gas in the tube.When the gas condition and the piston movement speed meet the appropriate condition-s,we use the method of front tracking to prove the piston problem described by the p-system initial boundary value problem has a global solution.This article is divided into several parts.First,we turn the problem into the Lagrangian coordinates.Second,we explain the solvability of various Riemann problems by implicit function theorem.Third,we solve the typical Riemann problem yields the solution of the interaction be-tween the waves.Fourth,we choose the proper weight to construct the Glimm function to guarantee the decreasing of Glimm functional.In order to deal with the interaction between the weak wave and the large rarefaction wave,we make appropriate change of Glimm functional.