Lipschitz metric for the Hunter-Saxton equation

Alberto Bressan, Helge Holden, Xavier Raynaud

Research output: Contribution to journalArticlepeer-review

34 Scopus citations

Abstract

We study stability of solutions of the Cauchy problem for the Hunter-Saxton equation ut+uux=14(∫-∞xux2dx-∫x∞ux2dx) with initial data u0. In particular, we derive a new Lipschitz metric dD with the property that for two solutions u and v of the equation we have dD(u(t),v(t))≥eCtdD(u0,v0).

Original languageEnglish (US)
Pages (from-to)68-92
Number of pages25
JournalJournal des Mathematiques Pures et Appliquees
Volume94
Issue number1
DOIs
StatePublished - Jul 2010

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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