Geodesic
Nonlocal problems for one-dimensional hyperbolic equation
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 24 (2018) no. 4, pp. 19-23 Cet article a éte moissonné depuis la source Math-Net.Ru

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This article discusses some nonlocal problems and methods of proving solvability of them. We show that choosing of effective method depends on the form of nonlocal conditions. One of these methods is based on reducing nonlocal problem to a boundary-value problem for a loaded equation and allows us to use many well-known methods of justification solvability. In the article, we consider the problem with nonlocal integral conditions for a one-dimensional hyperbolic equation and prove the equivalence to a problem with classical boundary conditions for a loaded equation.
Keywords: nonlocal problem, integral condition, hyperbolic equation, loaded equation. 
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V. A. Kirichek. Nonlocal problems for one-dimensional hyperbolic equation. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 24 (2018) no. 4, pp. 19-23. http://geodesic.mathdoc.fr/item/VSGU_2018_24_4_a2/

[1] Nahushev A. M., “On the Darboux problem for a nondegenerate loaded integrodifferential equation of the second order”, Differential Equations, 12:1 (1976), 103–108 | MR | Zbl

[2] Nahushev A. M., Equations of mathematical biology, Vysshaya shkola, M., 1995, 301 pp.

[3] Nahushev A. M., Loaded equations and their applications, Nauka, M., 2012, 232 pp. (in Russian)

[4] Pulkina L. S., “Boundary value problems for a hyperbolic equation with nonlocal conditions of the I and II kind”, Russian Mathematics (Iz. VUZ), 2012, no. 4, 74–83 (in Russian) | MR | Zbl

[5] Ladyzhenskaya O. A., Boundary problems of mathematical physics, Nauka, M., 1973, 407 pp. (in Russian)

[6] Dyuzheva A. V., “On certain nonlocal problem for hyperbolic equation with integral conditions of the first kind”, Vestnik of Samara State University. Natural Science Series, 2011, no. 5(86), 29–36 (in Russian)

[7] Beilina N. V., “Nonlocal problem with integral condition for a fourth order equation”, Vestnik of Samara State University. Natural Science Series, 2014, no. 10(121), 26–37 (in Russian) | Zbl

[8] Strigun M. V., “On certain nonlocal problem with integral boundary condition for hyperbolic equation”, Vestnik of Samara State University. Natural Science Series, 2009, no. 8(74), 78–87 (in Russian)

[9] Kozhanov A. I., “A time-nonlocal boundary problem for linear parabolic equations”, Journal of Applied and Industrial Mathematics, 7:1 (2004), 51–60 (in Russian) | Zbl

[10] Avalishvili G., Avalishvili M., Gordeziani D., “On integral nonlocal boundary value problems for some partial differential equations”, Bulletin of the Georgian National Academy of Science, 5:1 (2011), 31–37 http://science.org.ge/old/moambe/5-1/31-37 | Zbl