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Volume 3, Issue 2
A Local Inverse Conical Shock Problem for the Steady Supersonic Potential Flow

Yongqian Zhang

DOI: 10.4208/cmaa.2024-0012

Commun. Math. Anal. Appl., 3 (2024), pp. 287-313.

Published online: 2024-07

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  • Abstract

This paper studies an inverse problem of reconstructing the shape of the circular symmetric cone for the given leading shock front. Assuming that the attack angle is small and that the incoming flow has a large Mach Number, we show that the shape of the cone can be reconstructed near the vertex from the data of the given shock and establish an asymptotic expansion for the velocity and the slope of cone.

  • Keywords

Inverse problem, steady supersonic potential flow, conical shock, cone.

  • AMS Subject Headings

35L67, 35L65, 76J20, 76K05, 76L05, 76M21

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMAA-3-287, author = {Zhang , Yongqian}, title = {A Local Inverse Conical Shock Problem for the Steady Supersonic Potential Flow}, journal = {Communications in Mathematical Analysis and Applications}, year = {2024}, volume = {3}, number = {2}, pages = {287--313}, abstract = {

This paper studies an inverse problem of reconstructing the shape of the circular symmetric cone for the given leading shock front. Assuming that the attack angle is small and that the incoming flow has a large Mach Number, we show that the shape of the cone can be reconstructed near the vertex from the data of the given shock and establish an asymptotic expansion for the velocity and the slope of cone.

}, issn = {2790-1939}, doi = {https://doi.org/10.4208/cmaa.2024-0012}, url = {http://global-sci.org/intro/article_detail/cmaa/23230.html} }
TY - JOUR T1 - A Local Inverse Conical Shock Problem for the Steady Supersonic Potential Flow AU - Zhang , Yongqian JO - Communications in Mathematical Analysis and Applications VL - 2 SP - 287 EP - 313 PY - 2024 DA - 2024/07 SN - 3 DO - http://doi.org/10.4208/cmaa.2024-0012 UR - https://global-sci.org/intro/article_detail/cmaa/23230.html KW - Inverse problem, steady supersonic potential flow, conical shock, cone. AB -

This paper studies an inverse problem of reconstructing the shape of the circular symmetric cone for the given leading shock front. Assuming that the attack angle is small and that the incoming flow has a large Mach Number, we show that the shape of the cone can be reconstructed near the vertex from the data of the given shock and establish an asymptotic expansion for the velocity and the slope of cone.

Yongqian Zhang. (2024). A Local Inverse Conical Shock Problem for the Steady Supersonic Potential Flow. Communications in Mathematical Analysis and Applications. 3 (2). 287-313. doi:10.4208/cmaa.2024-0012
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