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Persistence properties and unique continuation of solutions to a two-component Camassa-Holm equation. (English) Zbl 1245.35108
Summary: We consider a two-component Camassa-Holm system which arises in shallow water theory. The present work is mainly concerned with persistence properties and unique continuation to this new kind of system, in view of the classical Camassa-Holm equation. Firstly, it is shown that there are three results about these properties of the strong solutions. Then we also investigate the infinite propagation speed in the sense that the corresponding solution does not have compact spatial support for t>0 although the initial data belongs to C 0 ().
35Q53KdV-like (Korteweg-de Vries) equations
35D35Strong solutions of PDE
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