Work

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

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.06317

Authors: Chen, Gui-Qiang G., Li, Qianfeng, Pu, Yun, Zhang, Yongqian

Language: English

Topic: Computational Fluid Dynamics and Aerodynamics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: Deutscher Akademischer Austauschdienst, National Natural Science Foundation of China, China Scholarship Council, Engineering and Physical Sciences Research Council

Awards: DMS-EPSRC: Stability Analysis for Nonlinear Partial Differential Equations across Multiscale Applications, G320558842, G4550331559, G5699805345, G7263143520, G8514182365

OpenAlex ID: W7212079314

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