Abstract
We consider a kind of Goursat problem for a fourth-order equation in a form not studied yet and prove the existence and uniqueness of the solution of this problem.
References
Myshkis, A.D., Lineinye differentsial’nye uravneniya s zapazdyvayushchim argumentom (Linear Differential Equations with Retarded Argument), Moscow: Nauka, 1972.
Myshkis, A.D., Some Problems in the Theory of Differential Equations with Deviating Argument, Uspekhi Mat. Nauk, 1977, vol. 32, no. 2, pp. 173–202.
Azbelev, N.V. and Rakhmatullina, L.F., Functional-Differential Equations, Differ. Uravn., 1978, vol. 14, no. 5, pp. 771–797.
Hale, J., Theory of Functional Differential Equations, New York: Springer, 1977. Translated under the title Teoriya funktsional’no-differentsial’nykh uravnenii, Moscow: Mir, 1984.
Mokeichev, V.S., Differentsial’nye uravneniya s otklonyayushchimsya argumentom (Differential Equations with Deviating Argument), Kazan, 1985.
Zarubin, A.N., Uravneniya smeshannogo tipa s zapazdyvayushchim argumentom: Uchebnoe posobie (Equations of Mixed Type with Retarded Argument: Students’ Book), Orel, 1997.
Zhegalov, V.I., A Characteristic Boundary Value Problem for a Hyperbolic Equation with Shifted Arguments of the Unknown Function, Dokl. Akad. Nauk, 2012, vol. 146, no. 5, pp. 490–493.
Andreev, A.A., On Analogues of Classical Boundary Value Problems for a Second-Order Differential Equation with Deviating Argument, Differ. Uravn., 2004, vol. 40, no. 5, pp. 1126–1128.
Andreev, A.A. and Saushkin, I.N., On an Analogue of the Tricomi Problem for a CertainModel Equation with Involutive Deviation in Infinite Domain, Vestn. Samar. Gos. Tekhn. Univ. Fiz.-Mat. Nauki, 2005, vol. 34, pp. 10–16.
Utkina, E.A., On a Certain Partial Differential Equation of the Fourth Order, Deposited in VINITI, 1999, no. 2059-V99.
Soldatov, A.P. and Shkhanukov, M.Kh., Boundary Value Problems with A. A. Samarskii’s General Nonlocal Condition for Higher-Order Pseudoparabolic Equations, Dokl. Akad. Nauk SSSR, 1987, vol. 297, no. 3, pp. 547–552.
Kolmogorov, A.N. and Fomin, S.V., Elementy teorii funktsii i funktsional’nogo analiza (Elements of the Theory of Functions and Functional Analysis), Moscow: Nauka, 1976.
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Original Russian Text © E.A. Utkina, 2015, published in Differentsial’nye Uravneniya, 2015, Vol. 51, No. 3, pp. 421–424.
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Utkina, E.A. Characteristic boundary value problem for a fourth-order equation with a pseudoparabolic operator and with shifted arguments of the unknown function. Diff Equat 51, 426–429 (2015). https://doi.org/10.1134/S0012266115030143
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DOI: https://doi.org/10.1134/S0012266115030143