This article is cited in 5 papers

Differential Equations and Mathematical Physics

The problem with shift for a degenerate hyperbolic equation of the first kind

Zh. A. Balkizov

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

Abstract: For a degenerate first-order hyperbolic equation of the second order containing a term with a lower derivative, we study two boundary value problems with an offset that generalize the well-known first and second Darboux problems. Theorems on an existence of the unique regular solution of problems are proved under certain conditions on given functions and parameters included in the formulation of the problems under study. The properties of all regular solutions of the equation under consideration are revealed, which are analogues of the mean value theorems for the wave equation.

Keywords: degenerate hyperbolic equations, Goursat problem, Darboux problem, problem with shift, mean value theorem.

UDC: 517.956.326

MSC: 35L80, 35L81

Received: April 20, 2020
Revised: February 12, 2021
Accepted: March 10, 2021
First online: March 29, 2021

DOI: 10.14498/vsgtu1783

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