On the Convergence of the Convectively Filtered Burgers Equation to the   Entropy Solution of the Inviscid Burgers Equation
  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. 
Greg Norgard and Kamran Mohseni