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Inheritance of Generic Singularities of Solutions of a Linear Wave Equation by Solutions of Isoentropic Gas Motion Equations

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Abstract

It is shown that the catastrophe germs of smooth mappings determining the three generic (in the sense of mathematical catastrophe theory) singularities of solutions of systems of equations for a one-dimensional isoentropic gas coincide with the germs corresponding to similar singularities of solutions of a linear wave equation with constant coefficients. The conjecture is put forth that such an inheritance for generic singularities of solutions of systems of equations for a isoentropic gas must also take place in spatially multidimensional cases.

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Acknowledgments

The authors thank I. A. Bogaevskii for very useful discussions and advice.

Funding

The work of A. M. Shavlukov was supported by the Russian Science Foundation under grant 21-11- 00006.

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Authors and Affiliations

  1. Institute of Mathematics with Computing Center of Ufa Federal Research Center of Russian Academy of Sciences, Ufa, 450008, Russia

    B. I. Suleimanov & A. M. Shavlukov

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  1. B. I. Suleimanov
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  2. A. M. Shavlukov
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Correspondence to B. I. Suleimanov.

Additional information

Translated from Matematicheskie Zametki, 2022, Vol. 112, pp. 625–640 https://doi.org/10.4213/mzm13583.

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Suleimanov, B.I., Shavlukov, A.M. Inheritance of Generic Singularities of Solutions of a Linear Wave Equation by Solutions of Isoentropic Gas Motion Equations. Math Notes 112, 608–620 (2022). https://doi.org/10.1134/S0001434622090292

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