Weak solutions for a singular beam equation

TL;DR

This paper establishes the existence of weak solutions for a dynamic Gao beam equation with a moving Dirac mass, using regularization techniques to handle singularities in an infinite domain.

Contribution

It introduces a method to prove weak solutions for a singular beam equation with a moving mass, extending the analysis to infinite-length beams.

Findings

Existence of weak solutions under regularity assumptions

Solution obtained as limit of regularized problems

Applicable to infinite-length beam models

Abstract

This paper deals with a dynamic Gao beam of infinite length subjected to a moving concentrated Dirac mass. Under appropriate regularity assumptions on the initial data, the problem possesses a weak solution which is obtained as the limit of a sequence of solutions of regularized problems.