Abstract:
The formula for solution of a problem for an equation with the higher partial derivative of the general type is constructed using Riemann method. In this problem the solution is found in the characteristic parallelepiped with separated by the non-characteristic surface angle. The Cauchy conditions are given on the non-characteristic part of bound and the Goursat conditions are given on the characteristics adjacent to this bound.
Received 26.04.2007
Document Type:
Article
UDC:517.956
Language: Russian
Citation:
A. N. Mironov, “On Riemann method for solving a mixed problem”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2(15) (2007), 27–32
\Bibitem{Mir07}
\by A.~N.~Mironov
\paper On Riemann method for solving a mixed problem
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2007
\vol 2(15)
\pages 27--32
\mathnet{http://mi.mathnet.ru/vsgtu526}
\crossref{https://doi.org/10.14498/vsgtu526}
Linking options:
https://www.mathnet.ru/eng/vsgtu526
https://www.mathnet.ru/eng/vsgtu/v115/p27
This publication is cited in the following 11 articles:
V. I. Korzyuk, O. A. Kovnatskaya, “Zadacha Pikara na ploskosti dlya kvazilineinogo giperbolicheskogo uravneniya vtorogo poryadka”, Tr. In-ta matem., 31:1 (2023), 70–80
V. I. Korzyuk, O. A. Kovnatskaya, V. A. Sevastyuk, “Goursat's problem on the plane for a quasilinear hyperbolic equation”, Dokl. Akad. nauk, 66:4 (2022), 391
A. N. Mironov, L. B. Mironova, Yu. O. Yakovleva, “Metod Rimana dlya uravnenii s dominiruyuschei chastnoi proizvodnoi (obzor)”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 25:2 (2021), 207–240
Mironov A.N., Yakovleva Yu.O., “Constructing the Riemann-Hadamard Function For a Fourth-Order Bianchi Equation”, Differ. Equ., 57:9 (2021), 1142–1149
Mironov A.N. Mironova L.B., “Riemann-Hadamard Method For One System in Three-Dimensional Space”, Differ. Equ., 57:8 (2021), 1034–1041
V. I. Korzyuk, O. A. Kovnatskaya, V. P. Serikov, “Zadachi dlya odnomernogo volnovogo uravneniya s usloviyami na kharakteristikakh i nekharakteristicheskikh liniyakh”, Tr. In-ta matem., 29:1-2 (2021), 106–112
I. G. Mamedov, “O neklassicheskoi traktovke chetyrekhmernoi zadachi Gursa dlya odnogo giperbolicheskogo uravneniya”, Vladikavk. matem. zhurn., 17:4 (2015), 59–66
A. Sopuev, N. K. Arkabaev, “Zadachi sopryazheniya dlya lineinykh psevdoparabolicheskikh uravnenii tretego poryadka”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2013, no. 1(21), 16–23
Ilgar G. Mamedov, On four-dimensional Goursat problem in the non-classical treatment for a hyperbolic equation [O neklassicheskoi traktovke chetyrekhmernoi zadachi Gursa dlya odnogo giperbolicheskogo uravneniya], 2013, 21 pp., arXiv: 1303.1036 [math.CA] (In Russian)
A. N. Mironov, “Application of the Riemann method to a factorized equation in an n-dimensional space”, Russian Math. (Iz. VUZ), 56:1 (2012), 48–54
I. G. Mamedov, “Zadacha Gursa novogo tipa dlya odnogo chetyrekhmernogo uravneniya so starshei chastnoi proizvodnoi”, Trudy sedmoi Vserossiiskoi nauchnoi konferentsii s mezhdunarodnym uchastiem (3–6 iyunya 2010 g.). Chast 3, Differentsialnye uravneniya i kraevye zadachi, Matem. modelirovanie i kraev. zadachi, Samarskii gosudarstvennyi tekhnicheskii universitet, Samara, 2010, 167–170
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