Abstract
We study the 1-D piston problem for compressible Euler equations under the assumptions that the total variations of the initial data and the piston velocity are both sufficiently small. By a modified Glimm scheme, we establish the global existence of entropy solutions including a strong shock wave without restriction on the strength.
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Acknowledgements
Funding was provided by Innovation Award from Wuhan University of Technology (Grant No. 20410771).
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Communicated by G.-Q. Chen
The research of Min Ding was supported in part by the Fundamental Research Funds for the Central Universities (WUT: 2018IB015 and 2018IVB013) and in part by the National Natural Science Foundation of China under Grant Nos. 11626176 and 11701435.
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Ding, M. Global Existence of Shock Front Solution to 1-D Piston Problem for Compressible Euler Equations. J. Math. Fluid Mech. 20, 2053–2071 (2018). https://doi.org/10.1007/s00021-018-0399-9
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DOI: https://doi.org/10.1007/s00021-018-0399-9