On Almost Entire Solutions Of The Burgers Equation

2016/11/18 by Nicholas D. Alikakos, Alikakos, Nicholas, Dimitrios Gazoulis +1
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Nonlinear Waves and Solitons #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1611.06166

openalex publication_date 2016/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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, H¹(S) = 0, are necessarily identically constant. We show this under the additional hypothesis that S is a subset of a countable union of ordered graphs.

Related

• A note on "New abundant solutions for the Burgers equation"
• Burgers' equation revisited: extension of mono-dimensional case on a network
• Classical Solutions for a Class of Burgers Equation
• Sharp ill-posedness and well-posedness results for the KdV-Burgers equation: the periodic case
• Beale-Kato-Majda type condition for Burgers equation