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PreprintCC BY 4.0arXiv

An Inverse Problem for Determining the Piston Speed from a Given Lipschitz Leading Shock

  • Gui-Qiang G. Chen
  • Qianfeng Li
  • Yun Pu
  • Yongqian Zhang
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Abstract

We analyze an inverse problem for determining the piston speed and the associated flow field from a prescribed leading shock and the initial data in a shock tube. The gas flow is described by the isentropic Euler equations (i.e., the p-system), while the trajectory of the leading shock is prescribed as a given Lipschitz curve. Under an Oleĭnik-type entropy condition on the leading shock, we develop a modified wavefront tracking scheme to construct the flow field behind the shock. This construction enables us to determine the corresponding piston speed and the associated flow field.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026inverse,
  title = {{An Inverse Problem for Determining the Piston Speed from a Given Lipschitz Leading Shock}},
  author = {Gui-Qiang G. Chen and Qianfeng Li and Yun Pu and Yongqian Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.06317},
  eprint = {2609.06317},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.06317},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - An Inverse Problem for Determining the Piston Speed from a Given Lipschitz Leading Shock
AU  - Gui-Qiang G. Chen
AU  - Qianfeng Li
AU  - Yun Pu
AU  - Yongqian Zhang
PY  - 2026
DA  - 2026/09/06
PB  - arXiv
DO  - 10.48550/arxiv.2609.06317
UR  - https://arxiv.org/abs/2609.06317
AB  - We analyze an inverse problem for determining the piston speed and the associated flow field from a prescribed leading shock and the initial data in a shock tube. The gas flow is described by the isentropic Euler equations (i.e., the p-system), while the trajectory of the leading shock is prescribed as a given Lipschitz curve. Under an Oleĭnik-type entropy condition on the leading shock, we develop a modified wavefront tracking scheme to construct the flow field behind the shock. This construction enables us to determine the corresponding piston speed and the associated flow field.
ER  -