Similarity Of Solutions Of Initial Boundary Value Problems For Two Special Gas Dynamical Equations

In this paper we compare the solution of the isentropic Euler equation and the patential flow equation with the same initial-boundary value which has small BV norm.For the initial-boundary value problem of the isentropic Euler equation,We can get its v-approximate solution by using wave-front tracking scheme,and the patential flow equation with the same initial-boundary value has a solution which consist of a Standard Riemann Semigroup.For any t>0,we prove that the L1norm of the difference between solutions to the isentropic Euler equation and the patential flow equation with the same initial-boundary value can be bounded by the cube of the total variation of the initial value and the boundary value.