Abstract
The article presents a solution to a boundary value problem for a fourth-order equation with multiple characteristics. The theorems of uniqueness, existence and existence of a regular solution of the problems are proved.
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REFERENCES
M. V. Turbin, ‘‘Investigation of the initial-boundary value problem for the Herschel–Bulkley fluid motion model,’’ Vestn. Voronezh. Univ., Ser. Fiz.-Mat. Nauk 2 (34), 246–257 (2013).
J. Whitham, Linear and Nonlinear Waves (Wiley Intersci., New York, 1974).
S. A. Shabrov, ‘‘On estimations of influence functions of one mathematical model of the fourth order,’’ Vestn. Voronezh. Univ., Ser. Fiz. Mat. 2, 168–179 (2015).
D. J. Benney and J. C. Luke, ‘‘Interactions of permanent waves of finite amplitude,’’ Math. Phys., No. 43, 309–313 (1964).
T. D. Dzhuraev and A. Sopuev, On the Theory of Differential Equations in Partial Derivatives of the Fourth Order (Fan, Tashkent, 2000).
D. Amanov and M. B. Murzambetova, ‘‘Boundary value problem for a fourth-order equation with a minor term,’’ Vestn. Udmurt. Univ., Mat. Mekh. Komp. Nauki, No. 1, 3–10 (2013).
D. Amanov, A. B. Bekiev, and Zh. A. Otarova, ‘‘Boundary value problem for a fourth-order equation,’’ Uzb. Math. Zh. 4, 11–18 (2015).
K. B. Sabitov, ‘‘Oscillations of a beam with closed ends,’’ Vestn. Samar. Tech. Univ., Ser. Fiz.-Mat. Nauki 19, 311–324 (2015).
B. Yu. Irgashev, ‘‘Boundary value problem for a high-order degenerate equation with lower terms,’’ Tr. Inst. Mat. 6, 23–29 (2019).
T. D. Dzhuraev and Yu. P. Apakov, ‘‘On the theory of the third-order equation with multiple characteristics containing the second time derivative,’’ Ukr. Math. J. 62, 43–55 (2010).
Yu. P. Apakov and S. Rutkauskas, ‘‘On a boundary problem to third order PDE with multiple characteristics,’’ Nonlin. Anal.: Model. Kontrol 16, 255–269 (2011).
Yu. P. Apakov, ‘‘On the solution of a boundary-value problem for a third-order equation with multiple characteristics,’’ Ukr. Math. J.64 (1), 1–11 (2012).
Yu. P. Apakov,‘‘On unique solvability of boundary-value problem for a viscous transonic equation,’’ Lobachevski J. Math. 41, 1754–1761 (2020).
Yu. P. Apakov and R. A. Umarov, ‘‘Solution of the boundary value problem for a third order equation with little terms construction of the Green’s function,’’ Lobachevskii J. Math. 43, 738–748 (2022). https://doi.org/10.1134/S199508022206004X
A. B. Bekiyev and T. M. Tadzhiev, ‘‘Study of a boundary value problem for a fourth order equation,’’ in Proceedings of the 4th International Conference on Nonlocal Boundary Value Problems and Related Problems of Mathematical Biology, Informatics and Physics, December 4–8, 2013, Nalchik, pp. 73–75.
D. Amanov and E. Skorobogatova, ‘‘Boundary value problem for the fourth order equation,’’ in World Mathematical Society of Turkish Countries: Proceedings of the 3rd Congress, Almaty, June 30–July 4, 2009 (2009), Vol. 4, p. 171.
Yu. P. Apakov and D. M. Meliquzieva, ‘‘Boundary value problem for a fourth-order equation with multiple characteristics,’’ Bull. NamGU, No. 5, 82–91 (2022).
B. M. Levitan and I. S. Sargsyan, Sturm–Liouville and Dirac Operators (Nauka, Moscow, 1988) [in Russian].
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Apakov, Y.P., Melikuzieva, D.M. On a Problem for a Fourth-Order Equation with Multiple Characteristics Containing the Third Time Derivate. Lobachevskii J Math 44, 3218–3224 (2023). https://doi.org/10.1134/S1995080223080061
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DOI: https://doi.org/10.1134/S1995080223080061