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Piston problems of two-dimensional Chaplygin gas. (English) Zbl 1435.35245

The authors consider the spatially two-dimensional piston problem for the isentropic Chaplygin gas. The piston is sharp, with straight edges (an angle) and slip boundary condition on the edges. The velocity of the piston is constant. Initial data are scaling-invariant. By the self-similarity transformation, the system is reduced to a 2D system. The authors prove existence of a piecewise smooth solution, describe the behaviour of the shocks depending on the Mach number for the piston moving into the gas, and the behaviour of the rarefaction waves and shocks for the piston moving out of the gas.

MSC:

35L65 Hyperbolic conservation laws
35L67 Shocks and singularities for hyperbolic equations
76L05 Shock waves and blast waves in fluid mechanics
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
83F05 Relativistic cosmology
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