Geodesic
Solvability of a non–local problem for a third—order equation with the heat operator in the main par
Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 30 (2020) no. 1, pp. 20-30 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, we considered the solvability of a nonlocal problem with integral condition for a thirdorder equation with head operatot in the main part. The existence and uniqueness of a regular solution to this problem are proved. The proof is based on reducing a non-local problem to the mixed problem for a loaded heat equation
Keywords: boundary–value problem, non–local problem, Green's function, Volterra integral equation.
Mots-clés : non–local condition, parabolic equation 
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O. S. Zikirov; M. M. Sagdullayeva. Solvability of a non–local problem for a third—order equation with the heat operator in the main par. Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 30 (2020) no. 1, pp. 20-30. http://geodesic.mathdoc.fr/item/VKAM_2020_30_1_a1/

[1] Barenblatt G. I., Zheltov Yu. P., Kochina I. N., “Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks”, J. Appl. Math. Mech., 24:5 (1960), 1286–1303 | Zbl

[2] Dzektser E. S., “Equation of motion of underground water with a free surface in multilayer media”, Soviet Physics Doklady, 20:3 (1975) | Zbl

[3] Chudnovsky A. F., Thermophysics of the soil, Nauka, Moscow, 1976, 352 pp.

[4] Golovanchikov A. B., Simonova I. E., Simonov B. V.,, “The solution of diffusion problem with integral boundary condition”, Fundam. Prikl. Mat., 7:2 (2001), 339–349 | MR | Zbl

[5] Cannon J.R. J., “The solution of the heat equation subject to the specification of energy”, Quart. Appl. Math., 21:2 (1963), 155 – 160 | DOI | MR

[6] Kamynin L. I., “A boundary value problem in the theory of heat conduction with a nonclassical boundary condition”, Zh. Vychisl. Mat. Mat. Fiz., 4:6 (1964), 33–59

[7] Ionkin N. I., “The solution of a certain boundary value problem of the theory of heat conduction with a nonclassical boundary condition”, Differ. Uravn., 13:2 (1977), 294–304 | MR | Zbl

[8] Ionkin N. I., Moiseev E. I., “A problem for a heat equation with two-point boundary conditions”, Differ. Uravn., 15:7 (1979), 1284–1295 | MR | Zbl

[9] Samarskii A. A., “Some problems of the theory of differential equations”, Differ. Uravn., 16:11 (1980), 1925–1935 | MR

[10] Yurchuk N. J., “A mixed problem with an integral condition for some parabolic equations”, Differ. Uravn, 22:12 (1986), 2117–2126 | MR | Zbl

[11] Kozhanov A. I. , “A time-nonlocal boundary value problem for linear parabolic equations”, Sib. Zh. Ind. Mat., 7:1 (2004), 51–60 | Zbl

[12] Dzhuraev T. D., Popelek Ya., “Classification and reduction to canonical form of third-order partial differential equations”, Differ. Equ., 27:10 (1991), 1225–1235 | MR

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

[14] Kozhanov A. I., Popov N. S., “On solvability to nonlocal boundary value problems for pseudoparabolic equations”, J. Math. Sci., 186:3 (2012), 438–452 | Zbl

[15] Nakhushev A. M., “Equations of mathematical biology”, Vysshaia shkola, 1995, 301 pp.

[16] Орынбасаров М. О., “Solution of a mixed problem for a third–order equation of composite type in a half-band”, Izv. NAN RK, Ser. Phis.–math., 2009, no. 1, 3-8

[17] Dzhuraev T. D., “Boundary value problems for the equations of mixed and mixed-composite types”, Fan Publ., Tashkent, 1979, 120 pp.