Lipschitz metric for the Hunter-Saxton equation

Alberto Bressan; Helge Holden; Xavier Raynaud

doi:10.1016/j.matpur.2010.02.005

Lipschitz metric for the Hunter-Saxton equation

Alberto Bressan, Helge Holden, Xavier Raynaud

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44 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 language	English (US)
Pages (from-to)	68-92
Number of pages	25
Journal	Journal des Mathematiques Pures et Appliquees
Volume	94
Issue number	1
DOIs	https://doi.org/10.1016/j.matpur.2010.02.005
State	Published - Jul 2010

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1016/j.matpur.2010.02.005

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title = "Lipschitz metric for the Hunter-Saxton equation",

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).",

author = "Alberto Bressan and Helge Holden and Xavier Raynaud",

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T1 - Lipschitz metric for the Hunter-Saxton equation

AU - Bressan, Alberto

AU - Holden, Helge

AU - Raynaud, Xavier

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N2 - 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).

AB - 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).

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JO - Journal des Mathematiques Pures et Appliquees

JF - Journal des Mathematiques Pures et Appliquees

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Lipschitz metric for the Hunter-Saxton equation

Abstract

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