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Zbl 1142.35078
Himonas, A.Alexandrou; Misiołek, Gerard; Ponce, Gustavo; Zhou, Yong
Persistence properties and unique continuation of solutions of the Camassa-Holm equation.
(English)
[J] Commun. Math. Phys. 271, No. 2, 511-522 (2007). ISSN 0010-3616; ISSN 1432-0916/e

The authors study the Camassa-Holm equation $$u_t - u_{txx} + 3uu_x -2u_x u_{xx} - u u_{xxx} = 0,$$ which physically was derived as a shallow water equation admitting peaked solitons. They prove that, given a strong solution to the Cauchy problem for this equation such that the initial data $u(x,0)$ decays exponentially together with the spatial derivative, if at some time $t_1>0$ the solution $u(x,t_1)$ decays exponentially in $x$ then $u$ is identically zero: $u(x,t) \equiv 0$.
[Iskander A. Taimanov (Novosibirsk)]
MSC 2000:
*35Q53 KdV-like equations
35Q35 Other equations arising in fluid mechanics
35B60 Continuation of solutions of PDE

Keywords: Camassa-Holm equation; Cauchy problem

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