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New Reductions of the Unsteady Axisymmetric Boundary Layer Equation to ODEs and Simpler PDEs

Author

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  • Alexander V. Aksenov

    (Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, 1 Leninskie Gory, Main Building, 119991 Moscow, Russia)

  • Anatoly A. Kozyrev

    (Dukhov All-Russia Research Institute of Automatics, Rosatom, 22 Suschevskaya St., 127055 Moscow, Russia)

Abstract

Reductions make it possible to reduce the solution of a PDE to solving an ODE. The best known are the traveling wave, self-similar and symmetry reductions. Classical and non-classical symmetries are also used to construct reductions, as is the Clarkson–Kruskal direct method. Recently, authors have proposed a method for constructing reductions of PDEs with two independent variables based on the idea of invariance. The proposed method in this work is a modification of the Clarkson–Kruskal direct method and expands the possibilities for its application. The main result of this article consists of a method for constructing reductions that generalizes the previously proposed approach to the case of three independent variables. The proposed method is used to construct reductions of the unsteady axisymmetric boundary layer equation to ODEs and simpler PDEs. All reductions of this equation were obtained.

Suggested Citation

  • Alexander V. Aksenov & Anatoly A. Kozyrev, 2022. "New Reductions of the Unsteady Axisymmetric Boundary Layer Equation to ODEs and Simpler PDEs," Mathematics, MDPI, vol. 10(10), pages 1-17, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:10:p:1673-:d:815078
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    Cited by:

    1. Alexander V. Aksenov & Anatoly A. Kozyrev, 2024. "Group Classification of the Unsteady Axisymmetric Boundary Layer Equation," Mathematics, MDPI, vol. 12(7), pages 1-10, March.

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