Переопределенная система дифференциальных уравнений в частных производных второго порядка с одной сингулярной точкой и одной граничной сверхсингулярной линией

Abstract

Redetermined system of second-order partial differential equations with one singular point and one boundary supersingular is considered in the paper. A solutions variety of redetermined systems of second-order partial differential equations with one singular point and one boundary supersingular line is found in explicit form with compatibility conditions accomplishment and three arbitrary constants using. An redetermined system of first order partial differential equations with one singular point is obtained by introducing a new function from the first two equations of this system into consideration. The general solution of this system is found in explicit form with one arbitrary constant using. Then a condition equivalent to the compatibility conditions of this system is obtained by substituting the general solution into the third equation of this system. If condition is performed, then a solution is reduced to a system of second-order ordinary differential equations with one supersingular line solving. A general solution of the redetermined system is found by resulting system solving in explicit form with three arbitrary constants using.