Stability of Rarefaction Wave to the 1-D Piston Problem for the Pressure-Gradient Equations

Abstract

The 1-D piston problem for the pressure gradient equations arising from the flux-splitting of the compressible Euler equations is considered. When the total variations of the initial data and the velocity of the piston are both sufficiently small, the author establishes the global existence of entropy solutions including a strong rarefaction wave without restriction on the strength by employing a modified wave front tracking method.

Keywords

Piston problem / Pressure gradient equations / Rarefaction wave / Wave front tracking method / Interaction of waves

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