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APPLICATION OF THE METHOD OF DIFFERENTIAL CONSTRAINTS TO SYSTEMS OF EQUATIONS WRITTEN IN RIEMANN INVARIANTS

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Abstract

Solutions of one-dimensional equations of gas dynamics and the equations describing the behavior of a nonlinear elastic material are reduced to solving a system of homogeneous differential equations written in Riemann invariants. It is shown that the solution of the Cauchy problem for such a system allowing for a differential constraint is reduced to solving a system of ordinary differential equations. Examples of solutions for certain initial data are given.

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Authors and Affiliations

  1. Suranaree University of Technology (SUT), Nakhon Ratchasima, 30000 Thailand, 30000, Nakhon Ratchasima, Thailand

    S. V. Meleshko & E. Shultz

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  1. S. V. Meleshko
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  2. E. Shultz
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Correspondence to S. V. Meleshko.

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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2021, Vol. 62, No. 3, pp. 5-14. https://doi.org/10.15372/PMTF20210301.

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Meleshko, S.V., Shultz, E. APPLICATION OF THE METHOD OF DIFFERENTIAL CONSTRAINTS TO SYSTEMS OF EQUATIONS WRITTEN IN RIEMANN INVARIANTS. J Appl Mech Tech Phy 62, 351–360 (2021). https://doi.org/10.1134/S0021894421030019

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  • DOI: https://doi.org/10.1134/S0021894421030019

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