Izv. Vyssh. Uchebn. Zaved. Mat., 2017, Number 5, Pages 11–25
This article is cited in 3 scientific papers (total in 3 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
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.
system of hyperbolic equations, nonlocal problem, integral condition, solvability, algorithm.
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Russian Mathematics (Izvestiya VUZ. Matematika), 2017, 61:5, 7–20
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
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\paper Nonlocal problem with integral conditions for a system of hyperbolic equations in characteristic rectangle
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\jour Russian Math. (Iz. VUZ)
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O. M. Kechina, “O razreshimosti nelokalnoi zadachi dlya uravneniya tretego poryadka”, Vestn. SamU. Estestvennonauchn. ser., 2017, no. 1, 15–20
Assanova A.T., “Solvability of a Nonlocal Problem For a Hyperbolic Equation With Integral Conditions”, Electron. J. Differ. Equ., 2017, 170
A. T. Assanova, B. Zh. Alikhanova, K. Zh. Nazarova, “Well-posedness of a nonlocal problem with integral conditions for third order system of the partial differential equations”, News Natl. Acad. Sci. Rep. Kazakhstan-Ser. Phys.-Math., 5:321 (2018), 33–41
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