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 language | English |
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Article number | 7016 |
Journal | Nonlinearity |
Volume | 33 |
Issue number | 12 |
Early online date | 23 Oct 2020 |
DOIs | |
Publication status | Published - 31 Oct 2020 |
Keywords
- Lie symmetries
- Nonlinear PDEs
- Singular solutions
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Applied Mathematics