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Ufimsk. Mat. Zh., 2017, Volume 9, Issue 2, Pages 25–39 (Mi ufa373)  

This article is cited in 1 scientific paper (total in 1 paper)

Dirichlet boundary value problem for a third order parabolic-hyperbolic equation with degenerating type and order in the hyperbolicity domain

Zh. A. Balkizov

Institute of Applied Mathematics and Automation, Nalchik

Abstract: In the work we study an analogue of Tricomi equation for a third order parabolic-hyperbolic equation with smaller derivatives having multiple characteristics. Under certain conditions for the given functions and parameters involved in the considered equation, we prove unique solvability theorem for the studied problem. The uniqueness of the solution is proved by means of the generalized Tricomi method, while the existence is proved via the method of integral equations.

Keywords: Degenerate hyperbolic equation, equation with multiple characteristics, third order parabolic-hyperbolic equation, Dirichlet boundary value problem, analogue of Tricomi equation, Tricomi method, second kind integral Volterra equation, second kind integral Fredholm equation.

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English version:
Ufa Mathematical Journal, 2017, 9:2, 25–39 (PDF, 394 kB); https://doi.org/10.13108/2017-9-2-25

Bibliographic databases:

MSC: 35M12
Received: 07.07.2016

Citation: Zh. A. Balkizov, “Dirichlet boundary value problem for a third order parabolic-hyperbolic equation with degenerating type and order in the hyperbolicity domain”, Ufimsk. Mat. Zh., 9:2 (2017), 25–39; Ufa Math. J., 9:2 (2017), 25–39

Citation in format AMSBIB
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\pages 25--39
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\pages 25--39
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. R. Kh. Makaova, “Kraevaya zadacha dlya giperbolicheskogo uravneniya tretego poryadka s vyrozhdeniem poryadka vnutri oblasti”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 21:4 (2017), 651–664  mathnet  crossref  zmath  elib
  • ”фимский математический журнал
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