This article is cited in 5 papers

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.

MSC: 35M12

Received: 07.07.2016

 English version: Ufa Mathematical Journal, 2017, 9:2, 25–39

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