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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arXiv · 2609.06317

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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Gui-Qiang G. Chen, Qianfeng Li, Yun Pu, Yongqian Zhang. 2026-09-06. An Inverse Problem for Determining the Piston Speed from a Given Lipschitz Leading Shock. https://arxiv.org/abs/2609.06317

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