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

Colin J. Cotter, Jacob Deasy, Tristan Pryer

Research output: Contribution to journalArticlepeer-review

4 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 languageEnglish
Article number7016
JournalNonlinearity
Volume33
Issue number12
Early online date23 Oct 2020
DOIs
Publication statusPublished - 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
  • Physics and Astronomy(all)
  • Applied Mathematics

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