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

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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.

About the authors

Zhiraslan A. Balkizov

Institute of Applied Mathematics and Automation
of Kabardin-Balkar Scientific Centre of RAS

Author for correspondence.
Email: giraslan@yandex.ru
ORCID iD: 0000-0001-5329-7766
SPIN-code: 1725-3008
Scopus Author ID: 57194853815
ResearcherId: K-2347-2018
http://www.mathnet.ru/rus/person41451

Cand. Phys. & Math. Sci.; Leading Researcher; Dept. of Mixed Type Equations

89 a, Shortanova st., Nal’chik, 360000, Russian Federation

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