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

Colin J. Cotter; Jacob Deasy; Tristan Pryer

doi:10.1088/1361-6544/abab4d

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

Colin J. Cotter, Jacob Deasy, Tristan Pryer

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

6 Citations (SciVal)

Abstract

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 Lr. 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.

Original language	English
Article number	7016
Journal	Nonlinearity
Volume	33
Issue number	12
Early online date	23 Oct 2020
DOIs	https://doi.org/10.1088/1361-6544/abab4d
Publication status	Published - 31 Oct 2020

Bibliographical note

Publisher Copyright:
© 2020 IOP Publishing Ltd & London Mathematical Society.

Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

Keywords

Lie symmetries
Nonlinear PDEs
Singular solutions

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
General Physics and Astronomy
Applied Mathematics

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10.1088/1361-6544/abab4dLicence: CC BY

Cite this

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AB - 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 Lr. 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.

KW - Lie symmetries

KW - Nonlinear PDEs

KW - Singular solutions

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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