Persistence Properties and Unique Continuation of Solutions of the Camassa-Holm Equation
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It is shown that a strong solution of the Camassa-Holm equation, initially decaying exponentially together with its spacial derivative, must be identically equal to zero if it also decays exponentially at a later time. In particular, a strong solution of the Cauchy problem with compact initial profile can not be compactly supported at any later time unless it is the zero solution.
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- DKT.De Lellis, C., Kappeler, T., Topalov, P.: Low-regularity solutions of the periodic Camassa-Holm equation. Comm. Partial Differential Equations (to appear) (2007)Google Scholar
- EKPV2.Escauriaza, L., Kenig, C. E., Ponce, G., Vega, L.: On uniqueness properties of solutions of the k-generalized KdV equations. J. Funct. Anal. (to appear) (2006)Google Scholar
- Z.Zhou, Y.: Infinite propagation speed for a shallow water equation. Preprint, available at http://www.fim.math.ethz.ch/preprints/2005/zhou.pdf, 2005Google Scholar