科研之友
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摘要
We study stability of solutions of the Cauchy problem on the line for the Camassa-Holm equation u(t) - u(xxt) + 3uu(x) - 2u(x)u(xx) - uu(xxx) = 0 with initial data u(0). In particular, we derive a new Lipschitz metric d(D) with the property that for two solutions u and v of the equation we have d(D)(u(t), v(t)) %26lt;= e(Ct)d(D)(u(0), v(0)). The relationship between this metric and the usual norms in H-1 and L-infinity is clarified. The method extends to the generalized hyperelastic-rod equation u(t) - u(xxt) + f(u)(x) - f(u)(xxx) + (g(u) + 1/2f %26apos;%26apos;(u)(u(x))(2))(x) = 0 (for f without inflection points).
- 出版日期2013-7
