Mots-clés : Goursat problem, Volterra equation.
@article{VNGU_2016_16_2_a2,
author = {O. S. Zikirov},
title = {On solvability non-local boundary value problem for the hyperbolic equation of the third order},
journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
pages = {16--25},
year = {2016},
volume = {16},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VNGU_2016_16_2_a2/}
}
TY - JOUR AU - O. S. Zikirov TI - On solvability non-local boundary value problem for the hyperbolic equation of the third order JO - Sibirskij žurnal čistoj i prikladnoj matematiki PY - 2016 SP - 16 EP - 25 VL - 16 IS - 2 UR - http://geodesic.mathdoc.fr/item/VNGU_2016_16_2_a2/ LA - ru ID - VNGU_2016_16_2_a2 ER -
O. S. Zikirov. On solvability non-local boundary value problem for the hyperbolic equation of the third order. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 16 (2016) no. 2, pp. 16-25. http://geodesic.mathdoc.fr/item/VNGU_2016_16_2_a2/
[1] G. N. Barenblatt, Yu. P. Zheltov, I. N. Kochina, “On the basic notions of the theory of homogeneous filtration of fluids in fractured rocks”, Prikl. Mat. Mekh., 24:5 (1960), 852–864 (in Russian) | MR | Zbl
[2] E. S. Dzektser, “Equations of groundwater with a free surface in a multi-layer media”, Dokl. AN SSSR, 220:3 (1975), 540–543 (in Russian) | Zbl
[3] A. F. Chudnovskiy, Thermal Physics of the Soils, Nauka, M., 1976 (in Russian)
[4] O. V. Rudenko, S. N. Soluyan, Theoretical Foundations of Nonlinear Acoustics, Nauka, M., 1975 (in Russian) | MR
[5] T. D. Dzhuraev, Ya. Popelek, “On the classification and reduction to canonical form of partial differential equations of the third order”, Differ. Uravn., 27:10 (1991), 1734–1745 (in Russian) | MR
[6] A. M. Nakhushev, The Problems with a Shift for the Main Types of Partial Differential Equations, Nauka, Novosibirsk, 2006 (in Russian)
[7] V. I. Zhegalov, A. N. Mironov, Differential Equations with Leading Partial Derivatives, Kazan, 2001 (in Russian)
[8] M. Kh. Shkhanukov, “Some boundary value problems for a third order equation appearing in the simulation of fluid flow in porous media”, Differ. Uravn., 18:4 (1982), 689–699 (in Russian) | MR | Zbl
[9] O. M. Dzhokhadze, “Influence of lower terms on the correctness of the characteristic problems for hyperbolic equations of the third order”, Mat. Zametki, 74:4 (2003), 517–528 (in Russian) | DOI | MR | Zbl
[10] Colton D., “Pseudo Parabolic Equations in One Space Variable”, J. of Differential Equations, 12:3 (1972), 559–565 | DOI | MR | Zbl
[11] Rundell W., “The Construction of Solutions to Pseudoparabolic Equations in Noncylindrical Domains”, J. of Differential Equations, 27:3 (1978), 394–404 | DOI | MR | Zbl
[12] V. A. Vodakhova, “Boundary value problem with nonlocal condition for a Nakhushev pseudoparabolic moisture transfer equation”, Differ. Uravn., 18:2 (1982), 280–285 (in Russian) | MR | Zbl
[13] A. A. Kerefev, E. V. Plotnikova, “Non-local problems for a third order equation”, Vladikavk. Mat. Zhur., 7:1 (2005), 51–60 (in Russian) | MR
[14] O. S. Zikirov, “Local and nonlocal boundary value problems for hyperbolic equations of the third order”, Sovr. Mat. i Prilozh., 68 (2011), 101–120 (in Russian) | MR