Piston problem for the isentropic Euler equations for a modified Chaplygin gas

We constructively solve the piston problem for one-dimensional isentropic Euler equations a modified Chaplygin gas. give rigorous proof of global existence and uniqueness shock wave separating constant states ahead when advances into The results are quite different from those pure gas or generalized gas, in which Radon measure solution is constructed to deal with concentration mass on piston. When recedes we show strictly that only first-family rarefaction exists front will never occur. In addition, by studying limiting behavior, solutions tend as single parameter pressure state function vanishes.