The r-Hunter-Saxton equation, smooth and singular solutions and their approximation
File(s)
Published version
Author(s)
Cotter, Colin J
Deasy, Jacob
Pryer, Tristan
Type
Journal Article
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.
Date Issued
2020-12-01
Date Acceptance
2020-07-31
Citation
Nonlinearity, 2020, 33 (12), pp.7016-7039
ISSN
0951-7715
Publisher
IOP Publishing
Start Page
7016
End Page
7039
Journal / Book Title
Nonlinearity
Volume
33
Issue
12
Copyright Statement
© 2020 IOP Publishing Ltd & London Mathematical Society. Original content from this work may be used under the terms of the Creative Commons
Attribution 3.0 licence. Any further distribution of this work must maintain attribution
to the author(s) and the title of the work, journal citation and DOI.
Attribution 3.0 licence. Any further distribution of this work must maintain attribution
to the author(s) and the title of the work, journal citation and DOI.
License URL
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000583992300001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Grant Number
EP/N023781/1
Subjects
Science & Technology
Physical Sciences
Mathematics, Applied
Physics, Mathematical
Mathematics
Physics
nonlinear PDEs
singular solutions
Lie symmetries
HYPERBOLIC VARIATIONAL EQUATION
GEODESIC-FLOW
Publication Status
Published
Date Publish Online
2020-10-23