Geodesic
The problem with shift for a degenerate hyperbolic equation of the first kind
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 25 (2021) no. 1, pp. 21-34

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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, Darboux problem, problem with shift, mean value theorem.
Mots-clés : Goursat problem 
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Zh. A. Balkizov. The problem with shift for a degenerate hyperbolic equation of the first kind. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 25 (2021) no. 1, pp. 21-34. http://geodesic.mathdoc.fr/item/VSGTU_2021_25_1_a1/