Open AccessOf one over determined system differential equation at private derivative second order with one singular point and one singular line
Author(s) -
Boitura Shoimkulov,
AUTHOR_ID
Publication year - 2021
Publication title -
vestnik permskogo universiteta. matematika, mehanika, informatika
Language(s) - English
Resource type - Journals
ISSN - 1993-0550
DOI - 10.17072/1993-0550-2021-4-14-18
Subject(s) - mathematics , singular solution , singular point of a curve , mathematical analysis , regular singular point , differential equation , partial differential equation , singular integral , boundary value problem , singular function , variety (cybernetics) , partial derivative , ordinary differential equation , integral equation , statistics
In this paper, a over determined system of second-order partial differential equations with one singular point and one singular line is investigated. A compatibility condition is found for over determined systems of second-order partial differential equations with one singular point and one singular line. 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. In this paper considers a redefined system of second-order partial differential equations, when the coefficients and right parts have one singular point and one singular line. Obtaining a variety of solutions and studying boundary value problems for linear differential equations of the hyperbolic type of the second order, some linear redefined systems of the first and second order with one and two supersingular lines and supersingular points is devoted to the monograph of academician of the National Academy of Sciences of the Republic of Tatarstan Rajabov N. - 1992 "Introduction to the theory of partial differential equations with supersingular coefficients" [6, p.126]. Using the obtained results of The monograph of Rajabov N., a variety of solutions of redefined systems of partial differential equations of the second order with one singular point and one singular line in an explicit form, through three arbitrary constants, was found.