CMMSE: Solutions in a Broad Sense to the Boundary Value Problem for First-Order Partial Differential Systems

Abstract

This article examines the initial-boundary value problem for a system of first-order partial differential equations. Issues of existence and uniqueness of the solution in a broad sense are considered, while taking into account both periodic and multipoint conditions. The definition of a solution in a broad sense is introduced; the initial problem is reduced to the initial-boundary value problem for ordinary differential equations. The two-point boundary value problem for ordinary differential equations systems is studied by the Dzhumabaev method (parameterization method), which allows us to move on to the equivalent multipoint boundary value problem with functional parameters. An algorithm to find an approximate solution to the problem in a broad sense has been developed.