Abstract:
We consider a boundary value problem for system of pseudo-hyperbolic equations of the fourth order with nonlocal condition on rectangular domain. By introducing new unknown function considered problem is reduced to equivalent nonlocal problem with integral condition for system of hyperbolic integro-differential equations of the second order. Algorithm for finding of approximate solution to equivalent problem is proposed and its convergence is proved on the basis method of functional parametrization. Sufficient conditions of the existence unique classical solution to boundary value problem for system of pseudo-hyperbolic equations of the fourth order with nonlocal condition are established in the terms of initial data.
Keywords:
system of pseudo-hyperbolic equations, nonlocal problem, system of hyperbolic integro-differential equations, integral condition, solvability.
Citation:
A. T. Assanova, Zh. S. Tokmurzin, “Boundary value problem for system of pseudo-hyperbolic equations of the fourth order with nonlocal condition”, Izv. Vyssh. Uchebn. Zaved. Mat., 2020, no. 9, 3–14; Russian Math. (Iz. VUZ), 64:9 (2020), 1–11
\Bibitem{AssTok20}
\by A.~T.~Assanova, Zh.~S.~Tokmurzin
\paper Boundary value problem for system of pseudo-hyperbolic equations of the fourth order with nonlocal condition
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2020
\issue 9
\pages 3--14
\mathnet{http://mi.mathnet.ru/ivm9607}
\crossref{https://doi.org/10.26907/0021-3446-2020-9-3-14}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2020
\vol 64
\issue 9
\pages 1--11
\crossref{https://doi.org/10.3103/S1066369X20090017}
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Linking options:
https://www.mathnet.ru/eng/ivm9607
https://www.mathnet.ru/eng/ivm/y2020/i9/p3
This publication is cited in the following 1 articles:
G. A. Abdikalikova, A. T. Assanova, Sh. T. Shekerbekova, “A nonlocal problem for fourth-order loaded hyperbolic equations”, Russian Math. (Iz. VUZ), 66:8 (2022), 1–18
Citation in format AMSBIB
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