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

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