On an integro-differential equation of pseudoparabolic-pseudohyperbolic type with degenerate kernels
Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 52 (2018) no. 1, pp. 19-26.

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In this article the questions of solvability of boundary value problem for a homogeneous pseudoparabolic-pseudohyperbolic type integro-differential equation with degenerate kernels are considered. Is used the Fourier method based on separation of variables. The criterion of one-value solvability of the considering problem is installed. Under this criterion is proved the one-valued solvability of the problem.
Keywords: integro-differential equation, mixed type equation, degenerate kernels, integral condition, one valued solvability.
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T. K. Yuldashev. On an integro-differential equation  of  pseudoparabolic-pseudohyperbolic type with  degenerate  kernels. Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 52 (2018) no. 1, pp. 19-26. http://geodesic.mathdoc.fr/item/UZERU_2018_52_1_a3/

[1] M. V. Turbin, “Investigation of Initial-Boundary Value Problem for the Herschel-Bulkley Mathematical Fluid Model.”, Vestnik of Voronezh State University. Physics, Mathematics, 2013, no. 2, 246–257 (in Russian)

[2] D. J. Benney, J. C. Luke, “Interactions of Permanent Waves of Finite Amplitude.”, Journ. Math. Phys., 1964, no. 43, 309–313 | DOI | MR

[3] M. Kh. Shkhanukov, “Some Boundary Value Problems for a Third-Order Equation Arising in the Simulation of Fluid Flow in Porous Media”, Differential Equations, 18:4 (1982), 689–699 (in Russian) | MR

[4] S. A. Shabrov, “Estimates of the Impact of a Mathematical Function of the Fourth-Order Model”, Vestnik of Voronezh State University. Physika, Matematika, 1 (2013), 232–250 (in Russian)

[5] G. B. Whitham, Linear and Nonlinear Waves, A Willey-Interscience Publication, N.Y.-London-Sydney-Toronto, 1974 | MR

[6] I. M. Gel'fand, “Some Questions of Analyses and Differential Equations”, Uspekhi Matematicheskikh Nauk, 14:3 (1959), 3–19 (in Russian) | MR

[7] F. I. Frankl, Selected Works in Gas Dynamics, Nauka, M., 1973, 711 pp. (in Russian) | MR

[8] Ya. S. Uflyand, “On the Question of the Distribution of Fluctuations in the Composite Electrical Lines”, Engineering Physics Journal, 7:1 (1964), 89–92 (in Russian)

[9] Yu. P. Apakov, “Three Dimensional Analog of Tricomi Problem for a Parabolo-Hyperbolic Equation”, Siberian Journal of Industrial Mathematics, 14:2 (2011), 34–44 (in Russian) | MR

[10] E. I. Moiseev, “Solvability of a Nonlocal Boundary Value Problem”, Differential Equations, 37:11 (2001), 1643–1646 | DOI | MR

[11] O. A. Repin, “An Analog of the Nakhushev Problem for the Bitsadze–Lykov Equation”, Differential Equations, 38:10 (2002), 1503–1508 | DOI | MR

[12] M. Kh. Ruziev, “On the Boundary-Value Problem for a Class of Equations of Mixed Type in an Unbounded Domain”, Math. Notes, 92:1 (2012), 70–78 | DOI | MR

[13] A. K. Urinov, Sh. T. Nishonova, “Problem with Integral Conditions for Elliptic-Parabolic Equations”, Math. Notes, 102:1 (2017), 68–80 | DOI | MR

[14] A. Sopuev, Dj. T. Djuraev, “Boundary Value problem for the Degenerating Parabolo-Hyperbolic Equation”, Differential Equations, 25:6 (1989), 68–80 | MR

[15] T. K. Yuldashev, “On a Mixed Type Differential Equation of Fourth Order”, Izvestia Instituta Matematiki i Informatiki UdGU, 47:1 (2016), 119–128 (in Russian) | MR | Zbl

[16] T. K. Yuldashev, “Nonlocal problem for a mixed type differential equation in rectangular domain”, Proceedings of the YSU, Physics Mathematics, 2016, no. 3, 70–78 | Zbl