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.
Citation:
Zh. A. Balkizov, “The problem with shift for a degenerate hyperbolic equation of the first kind”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 25:1 (2021), 21–34
\Bibitem{Bal21}
\by Zh.~A.~Balkizov
\paper The problem with shift for a degenerate hyperbolic equation of the first kind
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2021
\vol 25
\issue 1
\pages 21--34
\mathnet{http://mi.mathnet.ru/vsgtu1783}
\crossref{https://doi.org/10.14498/vsgtu1783}
\zmath{https://zbmath.org/?q=an:1474.35486}
\elib{https://elibrary.ru/item.asp?id=45604168}
Linking options:
https://www.mathnet.ru/eng/vsgtu1783
https://www.mathnet.ru/eng/vsgtu/v225/i1/p21
This publication is cited in the following 3 articles:
Zh. A. Balkizov, “Vnutrennekraevaya zadacha so smescheniem dlya smeshanno-giperbolicheskogo uravneniya vtorogo poryadka”, Doklady AMAN, 23:1 (2023), 11–19
Menglibay Kh. Ruziev, Nargiza T. Yuldasheva, “Nonlocal Boundary Value Problem for a Mixed Type Equation with Fractional Partial Derivative”, J Math Sci, 274:2 (2023), 275
Citation in format AMSBIB
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