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The multiplication of distributions in the study of delta shock waves for zero-pressure gasdynamics system with energy conservation laws

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Abstract

In this article, we study the delta shock wave for zero-pressure gasdynamics system with energy conservation laws in the frame of \(\alpha \)-solutions defined in the setting of distributional products. By reformulating the system, we construct within a convenient space of distributions, all solutions which include discontinuous solutions and Dirac delta measures. We also establish the generalized Rankine–Hugoniot jump conditions for delta shock waves. The \(\alpha \)-solutions which we constructed coincide with the solution obtained through different methods.

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Acknowledgements

The authors wish to thank Professor C. O. R. Sarrico for helpful suggestions to improve the manuscript. The first author (Anupam Sen), for the financial support, thanks University Grant Commission, Government of India (Sr. No. 2121540947, Ref No: 20/12/2015(ii)EU-V). The second author (TRS) would like to thank SERB, DST, Government of India (Ref. No. MTR/2019/001210) for financial support through MATRICS grant.

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  1. Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, India

    Anupam Sen & T. Raja Sekhar

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Sen, A., Raja Sekhar, T. The multiplication of distributions in the study of delta shock waves for zero-pressure gasdynamics system with energy conservation laws. Ricerche mat 72, 653–678 (2023). https://doi.org/10.1007/s11587-021-00565-5

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