The r-Hunter–Saxton equation, smooth and singular solutions and their approximation
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Peer-reviewed
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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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Journal Title
Nonlinearity
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Journal ISSN
0951-7715
1361-6544
1361-6544
Volume Title
33
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IOP Publishing
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Except where otherwised noted, this item's license is described as https://creativecommons.org/licenses/by/3.0/
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Engineering and Physical Sciences Research Council (EP/P000835/1 EP/R029423/1)