Geodesic
Solvability of some non--local problems for the loaded pseudoparabolic equation
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 77-88.

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In this paper we consider solvability of non–local problems for loaded pseudoparabolic equation of third order, with combine problems with integral conditions and problems with Steklov V.A. conditions with variable coefficients. The existence and uniqueness of classical solution of considered problem is proved by Riemann's method.
Keywords: loaded equation, Riemann function
Mots-clés : non–local condition, pseudoparabolic equation. 
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O. S. Zikirov; D. K. Kholikov. Solvability of some non--local problems for the loaded pseudoparabolic equation. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 77-88. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a79/

[1] M.T.Jenaliev, The theory of boundary value problems for loaded differential equations, Almaty, 1995 (In Russian)

[2] A.M. Nahushev, Equations of Mathematical Biology, Vysshaya shkola, M., 1995 (In Russian) | Zbl

[3] V.I. Zhegalov, A.N. Mironov, Differential equations with highest partial derivatives, Kazansk. Matem. Ob-vo, Kazan’, 2001 (In Russian) | Zbl

[4] G.N. Barenblatt, Yu. P. Zheltov, I. N. Kochina, “Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks (strata)”, PMM, J. Appl. Math. Mech., 24 (1961), 1286–1303 | DOI | Zbl

[5] E.S. Dzektser, “Equation of motion of underground water with a free surface in multilayer media”, Dokl. AN USSR, 220:3 (1975), 540–543 | Zbl

[6] A.F. Chudnovsky, Teplofizika pochv, Nauka, M., 1976 (In Russian)

[7] M. Kh. Shkhanukov, “On some boundary value problems for an equation of third order arising from simulation of filtration of a fluid in porous media”, Differ. Uravn., 18 (1982), 689–699 | MR | Zbl

[8] A.P. Soldatov, M. Kh. Shkhanukov, “Boundary value problems with general nonlocal Samarskij condition for pseudoparabolic equations of higher order”, Dokl. AN USSR, 297:3 (1987), 547–552 | MR | Zbl

[9] O.M. Dzhokhadze, “The Influence of the younger members on the correctness of characteristic problems for hyperbolic equations of third order”, Mat. notes, 74:4 (2003), 517–528 | MR | Zbl

[10] A.I. Kozhanov, N.S. Popov, “On the solvability of some problems with offset for pseudoparobolic equation”, J. Math. Sci., New York, 186:3 (2012), 438–452 | DOI | MR | Zbl

[11] A.A. Kerefov, Y.V. Plotnikova, “Nonlocal problems for a third-order equation”, Vladikavkaz Math. J., 7:1 (2005), 51–60 | MR | Zbl

[12] A. Bouziani, N. Merazga, “Solution to a semilinear pseudoparabolic problem with integral conditions”, Elect. J. Differ. Equ., 2006:115 (2006), 1–18 | MR | Zbl

[13] D.-Q. Dai, Y. Huang, “Nonlocal boundary problems for a third-order one-dimensional nonlinear pseudoparabolic equation”, Nonlinear Anal. Theory, Methods Appl., Ser. A, Theory Methods, 66:1 (2007), 179–191 | DOI | MR | Zbl

[14] L.S. Pulkina, “Nonlocal problem with two integral conditions for hyperbolic equation on plane”, Neklasicheskie uravneniya matematicheskoy fiziki, Novosibirsk, 2007, 232–236 (In Russian)

[15] A.I. Kozhanov, L.S. Pulkina, “On the solvability of boundary value problems with a nonlocal boundary condition of integral form for multidimensional hyperbolic equations”, Differ. Equ., 42:9 (2006), 1233–1246 | DOI | MR | Zbl

[16] V.A. Steklov, Osnovnie zadachi matematicheskoy fiziki, Nauka, M., 1983 (In Russian) | Zbl

[17] A. M. Nakhushev, Problems with shift for partial differential equations, Nauka, M., 2006 (In Russian) | MR | Zbl

[18] A.I. Kozhanov, “On a nonlocal boundary value problem with variable coefficients for the heat equation and the Aller equation”, Differ. Equ., 40:6 (2004), 815–826 | DOI | MR | Zbl

[19] O.S. Zikirov, D.K. Kholikov, “Nonlocal problems for loaded pseudoparabolic equation”, Neklasicheskie uravneniya matematicheskoy fiziki, Novosibirsk, 2010, 102–109 (In Russian)

[20] O.S. Zikirov, D.K. Kholikov, “On some problem for a loaded pseudoparabolic equation of the third order”, Mat. Zamet. SVFU, 23:2 (2016), 19–30 | MR | Zbl

[21] D.K. Kholikov, “On On one loaded partial-differential equation of the third order”, Neklasicheskie uravneniya matematicheskoy fiziki, Novosibirsk, 2012, 292–299 (In Russian)