The r-Hunter-Saxton equation, smooth and singular solutions and their approximation

In this work we introduce the r-Hunter-Saxton equation, a generalisation of the Hunter-Saxton equation arising as extremals of an action principle posed in L_r. We characterise solutions to the Cauchy problem, quantifying the blow-up time and studying various symmetry reductions. We construct piecew...

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Veröffentlicht in:	arXiv.org 2020-04
Hauptverfasser:	Cotter, Colin, Deasy, Jacob, Pryer, Tristan
Format:	Artikel
Sprache:	eng
Schlagworte:	Cauchy problems Linear functions Mathematics - Analysis of PDEs Physics - Exactly Solvable and Integrable Systems
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	In this work we introduce the r-Hunter-Saxton equation, a generalisation of the Hunter-Saxton equation arising as extremals of an action principle posed in L_r. 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 r-Hunter-Saxton equation.
ISSN:	2331-8422
DOI:	10.48550/arxiv.1911.09619