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An Inverse Problem for Determining the Shape of the Wedge in Steady Supersonic Potential Flow

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Abstract

This paper studies a problem of determining the shape of wedge in the planar steady supersonic potential flow. Assume that the pressure on the wedge is given with a small total variation and is close to the constant pressure of incoming flow, we use the Glimm scheme to construct approximate boundaries and corresponding approximate solutions and prove that approximate boundaries and the corresponding solutions have convergent subsequences. Then both the boundary of wedge and the corresponding global weak solution can be determined.

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Acknowledgements

The authors are grateful to the anonymous referees for useful comments and suggestions.

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  1. Yun Pu and Yongqian Zhang have contributed equally to this work.

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  1. School of Mathematical Sciences, Fudan University, 220 Handan Rd., Shanghai, 200433, People’s Republic of China

    Yun Pu & Yongqian Zhang

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  1. Yun Pu
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  2. Yongqian Zhang
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Correspondence to Yongqian Zhang.

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Pu, Y., Zhang, Y. An Inverse Problem for Determining the Shape of the Wedge in Steady Supersonic Potential Flow. J. Math. Fluid Mech. 25, 25 (2023). https://doi.org/10.1007/s00021-023-00768-w

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