Open AccessOn the solvability of a semi-periodic boundary value problem for the nonlinear Goursat equation
Author(s) -
N Orumbayeva,
AUTHOR_ID,
T.D. Tokmagambetova,
Zh.N. Nurgalieva,
AUTHOR_ID,
AUTHOR_ID
Publication year - 2021
Publication title -
ķaraġandy universitetìnìn̦ habaršysy. matematika seriâsy
Language(s) - English
Resource type - Journals
eISSN - 2663-5011
pISSN - 2518-7929
DOI - 10.31489/2021m4/110-117
Subject(s) - mathematics , boundary value problem , nonlinear system , constructive , ordinary differential equation , mathematical analysis , hyperbolic partial differential equation , partial differential equation , function (biology) , differential equation , initial value problem , free boundary problem , process (computing) , physics , quantum mechanics , evolutionary biology , computer science , biology , operating system
In this paper, by means of a change of variables, a nonlinear semi-periodic boundary value problem for the Goursat equation is reduced to a linear gravity problem for hyperbolic equations. Reintroducing a new function, the obtained problem is reduced to a family of boundary value problems for ordinary differential equations and functional relations. When solving a family of boundary value problems for ordinary differential equations, the parameterization method is used. The application of this approach made it possible to establish the coefficients of the unique solvability of the semi-periodic problem for the Goursat equation and to propose constructive algorithms for finding an approximate solution.