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

Published version
Peer-reviewed

Repository URI

https://www.repository.cam.ac.uk/handle/1810/311960

Repository DOI

https://doi.org/10.17863/CAM.59053
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Bibliographic metadata (7.78 KB)
 Published version (1001.5 KB)

Type

Article

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Authors

Cotter, Colin J  ORCID logo  https://orcid.org/0000-0001-7962-8324

Abstract

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 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.

Description

Keywords

Paper, nonlinear PDEs, singular solutions, Lie symmetries, 37K06, 37K58, 35Q53, 37K05

Journal Title

Nonlinearity

Conference Name

Journal ISSN

0951-7715
1361-6544

Volume Title

33

Publisher

IOP Publishing

Publisher DOI

https://doi.org/10.1088/1361-6544/abab4d

Rights and licensing

Attribution 3.0 Unported (CC BY 3.0)
Except where otherwised noted, this item's license is described as Attribution 3.0 Unported (CC BY 3.0)
Sponsorship
Engineering and Physical Sciences Research Council (EP/P000835/1 EP/R029423/1)

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