Nicholas D. Alikakos, Dimitrios Gazoulis
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,
, equal to zero.
We establish that under these conditions the solution is identically equal
to a constant.
Submitted November 21, 2016. Published February 20, 2018.
Math Subject Classifications: 35B08, 35L65.
Key Words: Burgers equation; entropy solution; rigidity.
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| Nicholas D. Alikakos Department of Mathematics, University of Athens panepistimioupolis 15784 Athens, Greece email: nalikako@math.uoa.gr |
| Dimitrios Gazoulis Department of Mathematics, University of Athens panepistimioupolis 15784 Athens, Greece email: dgazoulis@math.uoa.gr |
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