Singularities of a characteristic Cauchy problem for a PDE with singular coefficients

TL;DR

This paper provides explicit solutions for a class of PDEs with singular coefficients using hypergeometric functions, allowing detailed analysis of their singularities and analytic continuation.

Contribution

It introduces explicit solutions in terms of hypergeometric functions for PDEs with singular coefficients, facilitating the study of their singularities.

Findings

Explicit solutions expressed via Gauss hypergeometric functions

Analysis of singularities and analytic continuation of solutions

Illustrative examples demonstrating the methods

Abstract

In this paper we give an explicit representation of the solutions of a characteristic Cauchy problem for a class of PDEs with singular coefficients. We give the explicit solutions in terms of the Gauss hypergeometric functions, which enable us to study the singularities and the analytic continuation. Our results are illustrated through some examples.