On an overdetermined system of second order diffirential equations with singular point

F. M. Shamsudinov

Matematičeskaâ fizika i kompʹûternoe modelirovanie, no. 5 (2014), pp. 46-54

Résumé

In this paper we consider the over determined system of second order differential equations with a singular point. The system of equations (1) consists of a hyperbolic equation and one partial differential equation of second order with a singular point. The first equation of 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 equation, we obtain the compatibility conditions for the coefficients and right-hand sides. On the basis of the conditions of independence from the left side of the variable $y$, to determine any function $\phi_1 (x)$, we obtain an ordinary differential equation of the first order. Another arbitrary function $\psi_1 (y)$ is determined from the condition of the independence of the left part at the appropriate, passing to the limit.Thus, the obtained representing the solution manifold system using a single arbitrary function of one independent variable $y$ and one arbitrary constant study of properties of the solutions, as well as consider the problem of А.

Détail

Keywords: over determined system, singular equation, rectangle, variety of solutions, singular point.