The r-Hunter–Saxton equation, smooth and singular solutions and their approximation
Publication Date
2020-12-01Journal Title
Nonlinearity
ISSN
0951-7715
Publisher
IOP Publishing
Volume
33
Issue
12
Pages
7016-7039
Language
en
Type
Article
This Version
VoR
Metadata
Show full item recordCitation
Cotter, C. J., Deasy, J., & Pryer, T. (2020). The r-Hunter–Saxton equation, smooth and singular solutions and their approximation. Nonlinearity, 33 (12), 7016-7039. https://doi.org/10.1088/1361-6544/abab4d
Abstract
<jats:title>Abstract</jats:title>
<jats:p>In this work we introduce the <jats:italic>r</jats:italic>-Hunter–Saxton equation, a generalisation of the Hunter–Saxton equation arising as extremals of an action principle posed in <jats:italic>L</jats:italic>
<jats:sup>
<jats:italic>r</jats:italic>
</jats:sup>. We characterise solutions to the Cauchy problem, quantifying the blow-up time and studying various symmetry reductions. We construct piecewise linear functions and show that they are weak solutions to the <jats:italic>r</jats:italic>-Hunter–Saxton equation.</jats:p>
Keywords
Paper, nonlinear PDEs, singular solutions, Lie symmetries, 37K06, 37K58, 35Q53, 37K05
Sponsorship
Engineering and Physical Sciences Research Council (EP/P000835/1 EP/R029423/1)
Identifiers
nonabab4d, abab4d, non-104084.r1
External DOI: https://doi.org/10.1088/1361-6544/abab4d
This record's URL: https://www.repository.cam.ac.uk/handle/1810/333001
Rights
Licence:
https://creativecommons.org/licenses/by/3.0/
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