Almost entire solutions of the Burgers equation

Files
alikakos.pdf (176 KB)
Date
2018-02-20
Authors
Alikakos, Nicholas
Gazoulis, Dimitrios
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
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, H1(S), equal to zero. We establish that under these conditions the solution is identically equal to a constant.
Description
Keywords
Burgers equation, Entropy solution, Rigidity
Citation
Alikakos, N. D., & Gazoulis, D. (2018). Almost entire solutions of the Burgers equation. <i>Electronic Journal of Differential Equations, 2018</i>(53), pp. 1-6.
URI
https://hdl.handle.net/10877/15109
Collections
Electronic Journal of Differential Equations