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 Vestnik SamU. Estestvenno-Nauchnaya Ser., 2018, Issue 24, Issue 3, Pages 30–34 (Mi vsgu580)

Mathematics

The Cauchy problem for the hyperbolic differential equation of the third order

J. O. Yakovleva

Department of Higher Mathematics, Samara State Technical Universuty, 244, Molodogvardeyskaya Street, Samara, 443100, Russian Federation

Abstract: In the article the Cauchy problem for the third order hyperbolic differential equation with nonmultiple characteristics is considered on the plane of two independent variables. The differential equation has tree nonmultiple characteristics and this equation is strongly hyperbolic equation. The regular solution of the Cauchy problem for the hyperbolic differential equation of the third order with the nonmultiple characteristics is constructed in an explicit form, the solution is obtained by the method of general solutions. The solution of the Cauchy problem enables describing the propagation of initial displacement, initial velocity and initial acceleration.

Keywords: differential equation of the third order, hyperbolic equation of the third order, nonmultiple characteristics, method of common solutions, Cauchy problem, regular solution, initial displacement, initial velocity.

DOI: https://doi.org/10.18287/2541-7525-2018-24-3-30-34

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Full text: http://www.journals.ssau.ru/.../6450 (published under the terms of the Creative Commons Attribution 4.0 International License)
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Document Type: Article
UDC: 519.999

Citation: J. O. Yakovleva, “The Cauchy problem for the hyperbolic differential equation of the third order”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 24:3 (2018), 30–34

Citation in format AMSBIB
\Bibitem{Yak18} \by J.~O.~Yakovleva \paper The Cauchy problem for the hyperbolic differential equation of the third order \jour Vestnik SamU. Estestvenno-Nauchnaya Ser. \yr 2018 \vol 24 \issue 3 \pages 30--34 \mathnet{http://mi.mathnet.ru/vsgu580} \crossref{https://doi.org/10.18287/2541-7525-2018-24-3-30-34} \elib{http://elibrary.ru/item.asp?id=36731740}