English

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

Analysis of PDEs 2020-12-02 v2 Exactly Solvable and Integrable Systems

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.

Keywords

Cite

@article{arxiv.1911.09619,
  title  = {The r-Hunter-Saxton equation, smooth and singular solutions and their approximation},
  author = {Colin Cotter and Jacob Deasy and Tristan Pryer},
  journal= {arXiv preprint arXiv:1911.09619},
  year   = {2020}
}

Comments

Revised after referee comments

R2 v1 2026-06-23T12:23:39.641Z