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

Published 21 Nov 2019 in math.AP and nlin.SI | (1911.09619v2)

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.

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