Eternal Solutions Of The Burgers Equation

Nicholas Alikakos, Dimitrios Gazoulis

Published 2016-11-18Version 1

Solutions that satisfy classically the Burgers equation except, perhaps, on a closed set S of the plane of potential singularities whose Hausdorff 1-measure is zero, $H^1(S) = 0$, are necessarily identically constant. We show this under the additional hypothesis that $S$ is a subset of a finite union of smooth graphs.