Almost entire solutions of the Burgers equation

Abstract

We consider Burgers equation on the whole x-t plane. We require the solution to be classical everywhere, except possibly over a closed set S of potential singularities, which is (a) a subset of a countable union of ordered graphs of differentiable functions, (b) has one dimensional Hausdorff measure, $H^1(S)$, equal to zero. We establish that under these conditions the solution is identically equal to a constant.

Keywords

• Burgers equation
• entropy solution
• rigidity