Geodesic
On an overdetermined system
Matematičeskaâ fizika i kompʹûternoe modelirovanie, no. 6 (2016), pp. 99-107

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In this paper we consider the overdetermined system of second order differential equations with a singular point. The system of equations (1) consists of a hyperbolic equation and two partial differential equations of second order with a singular point. The first equation of the system (1) under certain conditions on the coefficients can be represented as a superposition of two first order differential operators. Solving this equation and substituting its value in the second and third equation to get together conditions on the coefficients and right-hand sides. On the basis of the conditions of independence from the left side of the variable $y$, to determine the arbitrary function $\varphi_1(x)$ we obtain the ordinary differential equation of the first order. Other arbitrary function $\psi_1(y)$ is determined from the condition that the right side of independence in appropriate, limiting transition. Thus, the obtained representation of the diversity of solutions using two arbitrary constants and studied properties of the resulting decisions.
Keywords: singular point, rectangle, variety of solutions, overdetermined system, unknown function. 
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     author = {Ph. M. Shamsudinov},
     title = {On an overdetermined system},
     journal = {Matemati\v{c}eska\^a fizika i kompʹ\^uternoe modelirovanie},
     pages = {99--107},
     publisher = {mathdoc},
     number = {6},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VVGUM_2016_6_a9/}
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Ph. M. Shamsudinov. On an overdetermined system. Matematičeskaâ fizika i kompʹûternoe modelirovanie, no. 6 (2016), pp. 99-107. http://geodesic.mathdoc.fr/item/VVGUM_2016_6_a9/