This article is cited in 5 papers

Differential Equations and Mathematical Physics

On a boundary value problem for a third-order parabolic-hyperbolic type equation with a displacement boundary condition in its hyperbolicity domain

Zh. A. Balkizov

Institute of Applied Mathematics and Automation of Kabardin-Balkar Scientific Centre of RAS, Nal'chik, 360000, Russian Federation

Abstract: In the article, we investigate a boundary-value problem with a third-order inhomogeneous parabolic-hyperbolic equation with a wave operator in a hyperbolicity domain. A linear combination with variable coefficients in terms of derivatives of the sought function on independent characteristics, as well as on the line of type and order changing is specified as a boundary condition. We have established necessary and sufficient conditions that guarantee existence and uniqueness of a regular solution to the problem under study. In some cases, a solution representation is written out explicitly.

Keywords: degenerate hyperbolic equation, equation with multiple characteristics, parabolic-hyperbolic equation of third order, problems with a shift.

UDC: 517.956.6

MSC: 35M12, 35M32

Received: April 24, 2019
Revised: November 19, 2019
Accepted: January 27, 2020
First online: May 27, 2020

Language: English

DOI: 10.14498/vsgtu1694

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