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

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

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 piecewi...

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Veröffentlicht in:Nonlinearity 2020-12, Vol.33 (12), p.7016-7039
Hauptverfasser: Cotter, Colin J, Deasy, Jacob, Pryer, Tristan
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Sprache:eng
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Lie symmetries
nonlinear PDEs
singular solutions
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creator Cotter, Colin J
Deasy, Jacob
Pryer, Tristan
description 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.
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subjects Lie symmetries
nonlinear PDEs
singular solutions
title The r-Hunter-Saxton equation, smooth and singular solutions and their approximation
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