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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2017, Number 5, Pages 11–25
(Mi ivm9233)
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This article is cited in 23 scientific papers (total in 23 papers)
Nonlocal problem with integral conditions for a system of hyperbolic equations in characteristic rectangle
A. T. Assanova Institute of Mathematics and Mathematical Modeling, Ministry of Education and Science, Republic of Kazakhstan, 125 Pushkin str., Almaty, 050010 Republic of Kazakhstan
Abstract:
We consider a nonlocal problem with integral conditions for a system of hyperbolic equations in rectangular domain. We investigate the questions of existence of unique classical solution to the problem under consideration and approaches of its construction. Sufficient conditions of unique solvability to the investigated problem are established in the terms of initial data. The nonlocal problem with integral conditions is reduced to an equivalent problem consisting of the Goursat problem for the system of hyperbolic equations with functional parameters and functional relations. We propose algorithms for finding a solution to the equivalent problem with functional parameters on the characteristics and prove their convergence. We also obtain the conditions of a unique solvability to the boundary-value problem with integral condition for the system of an ordinary differential equations. As an example, we consider the nonlocal boundary-value problem with integral conditions for two-dimensional system of hyperbolic equations.
Keywords:
system of hyperbolic equations, nonlocal problem, integral condition, solvability, algorithm.
Received: 09.12.2015
Citation:
A. T. Assanova, “Nonlocal problem with integral conditions for a system of hyperbolic equations in characteristic rectangle”, Izv. Vyssh. Uchebn. Zaved. Mat., 2017, no. 5, 11–25; Russian Math. (Iz. VUZ), 61:5 (2017), 7–20
Linking options:
https://www.mathnet.ru/eng/ivm9233 https://www.mathnet.ru/eng/ivm/y2017/i5/p11
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Abstract page: | 283 | Full-text PDF : | 87 | References: | 39 | First page: | 24 |
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