Quasilinear viscous approximations to scalar conservation laws

TL;DR

This paper proves that quasilinear viscous approximations converge to the entropy solution of scalar conservation laws on bounded domains, providing a rigorous foundation for numerical and analytical methods.

Contribution

It establishes the convergence of quasilinear parabolic viscous approximations to entropy solutions in bounded domains, extending previous results to more general settings.

Findings

Convergence of viscous approximations to entropy solutions

Applicability to scalar conservation laws in bounded domains

Rigorous mathematical proof of convergence

Abstract

We prove the convergence of quasilinear parabolic viscous approximations to the entropy solution (in the sense of Bardos-Leroux-Nedelec) of a scalar conservation law, considered on a bounded domain in $\R^d$.