Lipschitz Metric for the Periodic Camassa–holm Equation
نویسندگان
چکیده
We study stability of conservative solutions of the Cauchy problem for the periodic Camassa–Holm equation ut−uxxt +3uux−2uxuxx−uuxxx = 0 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)) ≤ edD(u0, v0). The relationship between this metric and usual norms in H1 per and L ∞ per is clarified.
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تاریخ انتشار 2010