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Infinite propagation speed for the Degasperis-Procesi equation. (English) Zbl 1094.35099
The author studies the Degasperis-Procesi equation given by \[ u_{t}-u_{txx}+4uu_{x}=3u_{x}u_{xx}+uu_{xxx},\;t\geq 0,\;x\in \mathbb{R}. \] He proves that if the initial data \(u_{0}\neq 0\) is a function in \(\mathbb{H} ^{4}(\mathbb{R)}\) with compact support then the classical solution \(u(.,t)\) has not this property.

MSC:
35Q35 PDEs in connection with fluid mechanics
35B35 Stability in context of PDEs
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