On Almost Entire Solutions Of The Burgers Equation
Nicholas Alikakos, Dimitrios Gazoulis

TL;DR
This paper proves that solutions to the Burgers equation that are smooth except on a set of potential singularities with zero Hausdorff 1-measure, constrained to a union of graphs, must be constant.
Contribution
It establishes that almost entire solutions with singularities on a specific set are necessarily trivial, extending understanding of solution regularity for the Burgers equation.
Findings
Solutions with singularities on sets of zero Hausdorff 1-measure are constant.
Singularities confined to countable unions of graphs imply trivial solutions.
Abstract
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, , are necessarily identically constant. We show this under the additional hypothesis that is a subset of a countable union of ordered graphs.
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Taxonomy
Topicsadvanced mathematical theories · Nonlinear Waves and Solitons · Nonlinear Partial Differential Equations
