Methods and Applications of Analysis

Volume 23 (2016)

Number 3

A Lipschitz metric for conservative solutions of the two-component Hunter–Saxton system

Pages: 215 – 232

DOI: https://dx.doi.org/10.4310/MAA.2016.v23.n3.a1

Author

Anders Nordli (Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway)

Abstract

We establish the existence of conservative solutions of the initial value problem of the two-component Hunter–Saxton system on the line. Furthermore we investigate the stability of these solutions by constructing a Lipschitz metric.

Keywords

two-component Hunter–Saxton system, conservative solutions, Lipschitz metric

2010 Mathematics Subject Classification

Primary 35B35, 35Q53. Secondary 35Q20.

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Published 9 November 2016