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Preprint 2009-022

Lipschitz metric for the Hunter–Saxton equation

Alberto Bressan, Helge Holden and Xavier Raynaud

Abstract: We study stability of solutions of the Cauchy problem for the Hunter–Saxton equation

ut+uux=(∫(−∞,x)ux2dx−∫(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).

Paper:
Available as PDF (431 Kbytes).
Author(s):
Alberto Bressan
Helge Holden
Xavier Raynaud
Publishing information:
Comments:
Submitted by:
; 2009-05-08.