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Self-Similar Solutions of a Multidimensional Degenerate Partial Differential Equation of the Third Order

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  • Ainur Ryskan

    (Institute of Mathematics, Physics and Informatics, Abai Kazakh National Pedagogical University, Almaty 050012, Kazakhstan
    School of Digital Technologies, Narxoz University, Almaty 050035, Kazakhstan
    These authors contributed equally to this work.)

  • Zafarjon Arzikulov

    (Department of Higher Mathematics, Fergana Polytechnic Institute, Fergana 150100, Uzbekistan
    These authors contributed equally to this work.)

  • Tuhtasin Ergashev

    (Department of Higher Mathematics, National Research University “TIIAME”, Tashkent 100000, Uzbekistan
    Department of Mathematics, Analysis, Logic and Discrete Mathematics, Ghent University, 9000 Gent, Belgium
    These authors contributed equally to this work.)

  • Abdumauvlen Berdyshev

    (Institute of Mathematics, Physics and Informatics, Abai Kazakh National Pedagogical University, Almaty 050012, Kazakhstan
    These authors contributed equally to this work.)

Abstract

When studying the boundary value problems’ solvability for some partial differential equations encountered in applied mathematics, we frequently need to create systems of partial differential equations and explicitly construct linearly independent solutions explicitly for these systems. Hypergeometric functions frequently serve as solutions that satisfy these systems. In this study, we develop self-similar solutions for a third-order multidimensional degenerate partial differential equation. These solutions are represented using a generalized confluent Kampé de Fériet hypergeometric function of the third order.

Suggested Citation

  • Ainur Ryskan & Zafarjon Arzikulov & Tuhtasin Ergashev & Abdumauvlen Berdyshev, 2024. "Self-Similar Solutions of a Multidimensional Degenerate Partial Differential Equation of the Third Order," Mathematics, MDPI, vol. 12(20), pages 1-13, October.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:20:p:3188-:d:1496833
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    References listed on IDEAS

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    1. Ashish Verma & Jihad Younis & Vikash Kumar Pandey & Hassen Aydi, 2021. "Some Summation Formulas for the Generalized Kampé de Fériet Function," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-11, September.
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