Results on modelling and products of singularities in Colombeau algebra G(R)

TL;DR

This paper systematically models singularities using Colombeau generalized functions and evaluates their products when associated distributions exist, aiding in the mathematical treatment of discontinuities in physical phenomena.

Contribution

It introduces a systematic approach to model singularities with Colombeau generalized functions and evaluates their products under certain conditions, advancing the mathematical framework for singularities.

Findings

Successful modeling of singularities using Colombeau algebra

Evaluation of products of singularity-modeling functions

Identification of conditions for associated distributions

Abstract

Modelling of singularities given by discontinuous functions or distributions by means of generalized functions has proved useful in many problems posed by physical phenomena. We introduce in a systematic way generalized functions of Colombeau that model such singularities. Moreover, we evaluate some products of singularity-modelling generalized functions whenever the result admits an associated distribution