Viscous Burgers equation driven by point source: a formula for the weak limit

TL;DR

This paper derives the weak limit of solutions to the viscous Burgers equation with a point source as viscosity vanishes, linking it to a novel variational problem involving three types of functionals.

Contribution

It introduces a new approach to analyze the zero-viscosity limit of Burgers equation with point sources, connecting it to a unique variational formulation.

Findings

Weak limit characterized by a variational problem

Novel connection between source term and functional types

Provides insights into singular source effects in PDEs

Abstract

In this article, we obtain the weak limit of the solutions of the viscous Burgers equation driven by a point source term, as the coefficient of viscosity tends to zero. The weak limit is related to the variational problem that consists of three types of functional, which is not usual in the absence of the source term.