51. The r-Hunter-Saxton equation, smooth and singular solutions and their approximation
- Author
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Colin J. Cotter, Tristan Pryer, Jacob Deasy, Cotter, Colin J [0000-0001-7962-8324], Apollo - University of Cambridge Repository, and Engineering & Physical Science Research Council (EPSRC)
- Subjects
Paper ,singular solutions ,GEODESIC-FLOW ,Work (thermodynamics) ,General Mathematics ,Mathematics, Applied ,HYPERBOLIC VARIATIONAL EQUATION ,Mathematics::Analysis of PDEs ,General Physics and Astronomy ,FOS: Physical sciences ,01 natural sciences ,Piecewise linear function ,37K06 ,Mathematics - Analysis of PDEs ,0102 Applied Mathematics ,37K05 ,FOS: Mathematics ,Hunter–Saxton equation ,Applied mathematics ,Initial value problem ,Lie symmetries ,0101 mathematics ,nlin.SI ,math.AP ,Mathematical Physics ,Mathematics ,Science & Technology ,Nonlinear Sciences - Exactly Solvable and Integrable Systems ,Physics ,Applied Mathematics ,010102 general mathematics ,4901 Applied Mathematics ,4904 Pure Mathematics ,Statistical and Nonlinear Physics ,Action (physics) ,Symmetry (physics) ,Physics, Mathematical ,010101 applied mathematics ,35Q53 ,Nonlinear Sciences::Exactly Solvable and Integrable Systems ,nonlinear PDEs ,Physical Sciences ,49 Mathematical Sciences ,37K58 ,Exactly Solvable and Integrable Systems (nlin.SI) ,Analysis of PDEs (math.AP) - 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
- Published
- 2019