A boundary value problem for nonlinear differential equation with arbitrary functions

Abstract

This article describes a semi-batch nonlinear boundary value problem for differential equations with partial derivatives. The equations containing arbitrary parameters were considered in Whitham G.B. Such equations are encountered in some problems of chemical technology and chromatography. Replacing u = e^kz in a nonlinear problem with arbitrary functions leads to a semi-batch linear boundary value problem for hyperbolic equations. Introducing a new unknown function, semi-batch linear boundary value problem for hyperbolic equations with mixed derivative reduced to the family of boundary value problems for ordinary differential equations and functional relation. Using the method of parameterization to the family of boundary value problems for ordinary differential equations, We find approximate solutions of equations in this area. The proposed method is illustrated by an example.