Abstract:
We seek for a solution to a system of
differential equations, using linear relations connecting normal derivatives of the desired functions at the domain boundary.
Keywords:
hyperbolic systems, boundary value problems, solvability conditions.
Citation:
V. I. Zhegalov, “A problem with normal derivatives in the boundary conditions for a system of differential equations”, Izv. Vyssh. Uchebn. Zaved. Mat., 2008, no. 8, 70–72; Russian Math. (Iz. VUZ), 52:8 (2008), 58–60
\Bibitem{Zhe08}
\by V.~I.~Zhegalov
\paper A problem with normal derivatives in the boundary conditions for a system of differential equations
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2008
\issue 8
\pages 70--72
\mathnet{http://mi.mathnet.ru/ivm1681}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2468316}
\zmath{https://zbmath.org/?q=an:1176.35115}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2008
\vol 52
\issue 8
\pages 58--60
\crossref{https://doi.org/10.3103/S1066369X08080070}
Linking options:
https://www.mathnet.ru/eng/ivm1681
https://www.mathnet.ru/eng/ivm/y2008/i8/p70
This publication is cited in the following 9 articles:
A. N. Mironov, E. F. Koskova, “O zadache s usloviyami na kharakteristikakh i svobodnoi poverkhnosti dlya giperbolicheskoi sistemy uravnenii s tremya nezavisimymi peremennymi s dvukratnymi kharakteristikami”, Izv. vuzov. Matem., 2025, no. 1, 28–36
E. A. Sozontova, “Usloviya suschestvovaniya i edinstvennosti resheniya zadachi Gursa dlya sistemy uravnenii s dominiruyuschimi chastnymi proizvodnymi”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 27:2 (2023), 375–383
A. N. Mironov, A. P. Volkov, “On the Darboux problem for a hyperbolic system of equations with multiple characteristics”, Russian Math. (Iz. VUZ), 66:8 (2022), 31–36
Mironov A.N. Mironova L.B., “Riemann-Hadamard Method For One System in Three-Dimensional Space”, Differ. Equ., 57:8 (2021), 1034–1041
Mironov A.N., “On Boundary Value Problems With Normal High-Order Derivatives on Characteristics”, AIP Conference Proceedings, 2328, ed. Grigorev Y. Popov S. Sharin E., Amer Inst Physics, 2021, 020007
L. B. Mironova, “Application of Riemann method to one system in three-dimensional space”, Russian Math. (Iz. VUZ), 63:6 (2019), 42–50
L. B. Mironova, “On class of integral equations with partial integrals and its applications”, Ufa Math. J., 11:3 (2019), 61–77
E. A. Sozontova, “Characteristic problems with normal derivatives for hyperbolic systems”, Russian Math. (Iz. VUZ), 57:10 (2013), 37–47
E. A. Sozontova, “O kharakteristicheskikh zadachakh dlya odnoi sistemy giperbolicheskogo tipa v trekhmernom prostranstve”, Vestn. SamGU. Estestvennonauchn. ser., 2013, no. 6(107), 74–84