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Статья
2020

Boundary Value Problem for System of Pseudo-Hyperbolic Equations of the Fourth Order with Nonlocal Condition


A. T. AssanovaA. T. Assanova, Zh. S. TokmurzinZh. S. Tokmurzin
Русская математика
https://doi.org/10.3103/S1066369X20090017
Abstract / Full Text

We consider a boundary value problem for a system of the fourth order pseudo-hyperbolic equations with nonlocal condition on a rectangular domain. By introducing a new unknown function, the considered problem is reduced to an equivalent nonlocal problem with integral condition for a system of hyperbolic integro-differential equations of the second order. We propose an algorithm for finding an approximate solution to the equivalent problem, and its convergence is proved basing on the functional parametrization method. Sufficient conditions of the unique existence of the classical solution to the boundary value problem for the system of the fourth order pseudo-hyperbolic equations with nonlocal condition are established in the terms of initial data.

Author information
  • Institute of Mathematics and Mathematical Modeling,Ministry of Education and Science Republic of Kazakhstan, 125 Pushkin str., 050010, Almaty, Republic of KazakhstanA. T. Assanova
  • K. Zhubanov Aktobe Regional University, 34 A. Moldagulova Ave., 030000, Aktobe, Republic of KazakhstanZh. S. Tokmurzin
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