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We study the piston problem of the compressible fluid flow with thegeneralized Chaplygin gas. Depending on the inferential critical value of Machnumber, we prove that, there exists an integral weak solution for theproceeding piston problem, consisting of a shock separating constant statesahead of the piston if Mach numbers less than this critical value, while asingular measure solution, with density containing a Dirac measure supported onthe piston, shall be proposed to solve the proceeding piston problem if Machnumbers greater than or equal to the critical value. For the receding pistonproblem, rarefaction wave solution always exists when the piston recedes fromthe gas with any constant speed. Moreover, the occurrence of vacuum state andthe convergence of solutions, as well as degeneration of equations are analyzedin the receding case as Mach number tends to infinity.

Measure solutions to piston problem for compressible fluid flow of generalized chaplygin gas