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

Ainur Ryskan (), Zafarjon Arzikulov, Tuhtasin Ergashev () and Abdumauvlen Berdyshev
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Ainur Ryskan: Institute of Mathematics, Physics and Informatics, Abai Kazakh National Pedagogical University, Almaty 050012, Kazakhstan
Zafarjon Arzikulov: Department of Higher Mathematics, Fergana Polytechnic Institute, Fergana 150100, Uzbekistan
Tuhtasin Ergashev: Department of Higher Mathematics, National Research University “TIIAME”, Tashkent 100000, Uzbekistan
Abdumauvlen Berdyshev: Institute of Mathematics, Physics and Informatics, Abai Kazakh National Pedagogical University, Almaty 050012, Kazakhstan

Mathematics, 2024, vol. 12, issue 20, 1-13

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.

Keywords: degenerate partial differential equation; self-similar solution; confluent hypergeometric function; generalized confluent Kampé de Fériet hypergeometric function; hypergeometric-type system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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