К теории переопределенных систем дифференциальных уравнений в частных производных второго порядка с одной сингулярной линией в общем случае

Abstract

In this paper, an over determined system of second-order partial differential equations with a single singular line in the General case is investigated. A compatibility condition is found for over determined systems of second-order partial differential equations with a single singular line in the General case. If the compatibility condition is met, integral representations of the variety of solutions are found explicitly in terms of three arbitrary constants, when the singular line is in the boundaries of the domain for which initial data problems (Cauchy-type Problems) can be set.