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.
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This work was supported by the National Natural Science Foundation of China (Nos. 11626176, 11701435) and the Fundamental Research Funds for the Central Universities of China (Nos. 2018IB015, 2018IVB013).
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Ding, M. Stability of Rarefaction Wave to the 1-D Piston Problem for the Pressure-Gradient Equations. Chin. Ann. Math. Ser. B 40, 161–186 (2019). https://doi.org/10.1007/s11401-019-0124-x
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DOI: https://doi.org/10.1007/s11401-019-0124-x
Keywords
- Piston problem
- Pressure gradient equations
- Rarefaction wave
- Wave front tracking method
- Interaction of waves