Geodesic
A nonlocal problem with integral conditions for one-dimensional biwave equation
Trudy Instituta matematiki, Tome 25 (2017) no. 2, pp. 91-105 Cet article a éte moissonné depuis la source Math-Net.Ru

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The main aim of this work is to consider classical solution of the nonlocal problem for a bi-wave equation with integral conditions of the first kind. The main goal is to show the method which allows to prove solvability of a nonlocal problem with integral conditions of the first kind. Under smoothness and matching conditions of the given functions, existence and uniqueness of the solution of the problem are proved. Moreover, making use of characteristics method, the analytical solution of the problem is provided as well. 
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V. I. Korzyuk; N. V. Vinh. A nonlocal problem with integral conditions for one-dimensional biwave equation. Trudy Instituta matematiki, Tome 25 (2017) no. 2, pp. 91-105. http://geodesic.mathdoc.fr/item/TIMB_2017_25_2_a8/

[1] X. Feng, M. Neilan, “Finite element methods for a bi-wave equation modeling d-wave superconductors”, J. Comput. Math., 28:3 (2010), 331–353 | MR | Zbl

[2] X. Feng, M. Neilan, “Discontinuous finite element methods for a bi-wave equation modeling d-wave superconductors”, Math. Comput., 80:275 (2011), 1303–1333 | DOI | MR | Zbl

[3] W. I. Fushchych, O. V. Roman, R. Z. Zhdanov, “Symmetry reduction and some exact solutions of nonlinear biwave equations”, Rep. Math. Phys., 37:2 (1996), 267–281 | DOI | MR | Zbl

[4] V. I. Korzyuk, E. S. Cheb, “The Cauchy problem for a fourth-order equation with a bi-wave operator”, Differential Equations, 43 (2007), 688–695 | DOI | MR | Zbl

[5] V. Korzyuk, O. Konopelko, E. Cheb, “Boundary-value problems for fourth-order equations of hyperbolic and composite types”, Journal of Mathematical Sciences, 171 (2010), 89–115 | DOI | MR | Zbl

[6] Korzyuk V. I., Vinh N. V., Minh N. T., “Classical solution of the Cauchy problem for biwave equation: Application of Fourier transform”, Mathematical Modelling and Analysis, 17:5 (2012), 630–641 | DOI | MR | Zbl

[7] Korzyuk V. I., Vinh N. V., “Classical solutions of mixed problems for the one-dimensional biwave equation”, Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series, 2016, no. 1, 69–79 (In Russian)

[8] Korzyuk V. I., Vinh N. V., “Classical solution of a problem with an integral condition for the one-dimensional biwave equation”, Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series, 2016, no. 3, 16–29 (In Russian)

[9] Korzyuk V. I., Vinh N. V., “Cauchy problem for some fourth-order nonstrictly hyperbolic equations”, Nanosystems: Physics, Chemistry, Mathematics, 7:5 (2016), 869–879 | DOI | Zbl

[10] V. I. Korzyuk, N. V. Vinh, N. T. Minh, “Conservation law for the Cauchy-Navier equation of elastodynamics wave via Fourier transform”, Tr. Inst. Mat., 24:1 (2016), 100–106 | MR

[11] N. I. Muskhelishvili, Some basic problems of the mathematical theory of elasticity, Noordhoff International Publishing, 2010 | MR

[12] Elena Obolashvili, Higher Order Partial Differential Equations in Clifford Analysis: Effective Solutions to Problems, Birkhauser, Basel, 2003 | MR | Zbl