Delta-problems for the generalized Euler-Darboux equation

TL;DR

This paper investigates Delta-problems for the generalized Euler-Darboux equation with negative parameters in a square, addressing boundary value issues involving singularities and extending the understanding of degenerate hyperbolic equations.

Contribution

It introduces new classes of boundary value problems, including Delta-problems with singularities, for the generalized Euler-Darboux equation in rectangular regions.

Findings

Formulation of Delta-problems with singularities in squares

Development of simple formulae for boundary conditions

Extension of boundary value problem theory for degenerate hyperbolic equations

Abstract

Degenerate hyperbolic equations are dealing with many important issues for applied nature. While a variety of degenerate equations and boundary conditions, successfully matched to these differential equation, most in the characteristic coordinates reduced to Euler-Darboux one. Some boundary value problems, in particular Cauchy problem, for the specified equation demanded the introduction of special classes in which formulae are simple and can be used to meet the new challenges, including Delta-problems in squares that contain singularity line for equation coefficients with data on adjacent or parallel sides of the square. In this short communication the generalized Euler-Darboux equation with negative parameters in the rectangular region is considered.