On the Convergence of the Convectively Filtered Burgers Equation to the Entropy Solution of the Inviscid Burgers Equation

Abstract

This document provides a proof that the solutions to the convectively filtered Burgers equation, will converge to the entropy solution of the inviscid Burgers equation when certain restrictions are put on the initial conditions. It does so by first establishing convergence to a weak solution of the inviscid Burgers equation and then showing that the weak solution is the entropy solution. Then the results are extended to encompass more general initial conditions.

Minor changes and typo corrections

Cited by in corpus (2)

• A New Regularization of the One-Dimensional Euler and Homentropic Euler Equations
• Numerical simulation of compressible flows using two-phase observable Euler equations