TY - JOUR
T1 - Lipschitz metric for the Hunter-Saxton equation
AU - Bressan, Alberto
AU - Holden, Helge
AU - Raynaud, Xavier
PY - 2010/7
Y1 - 2010/7
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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U2 - 10.1016/j.matpur.2010.02.005
DO - 10.1016/j.matpur.2010.02.005
M3 - Article
AN - SCOPUS:77953811019
VL - 94
SP - 68
EP - 92
JO - Journal des Mathematiques Pures et Appliquees
JF - Journal des Mathematiques Pures et Appliquees
SN - 0021-7824
IS - 1
ER -