This article is cited in 2 papers

Differential Equations and Mathematical Physics

Delta-problems for the generalized Euler–Darboux equation

I. N. Rodionova, V. M. Dolgopolov, M. V. Dolgopolov

Samara National Research University, Samara, 443086, Russian Federation

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.

Keywords: generalized Euler–Darboux equation, boundary value problem.

UDC: 517.956.3

MSC: 35L10, 35Q05

Received: July 14, 2017
Revised: September 8, 2017
Accepted: September 18, 2017
First online: September 22, 2017

Language: English

DOI: 10.14498/vsgtu1557

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ArXiv: 1801.02083