The r-Hunter-Saxton equation, smooth and singular solutions and their approximation
arXiv:1911.09619 · doi:10.1088/1361-6544/abab4d
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.
Revised after referee comments