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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 $$ u_{t}-u_{txx}+4uu_{x}=3u_{x}u_{xx}+uu_{xxx},\ t\geq 0,\ x\in \Bbb{R}.$$ He proves that if the initial data $u_{0}\neq 0$ is a function in $\Bbb{H} ^{4}(\Bbb{R)}$ with compact support then the classical solution $u(.,t)$ has not this property.

35Q35PDEs in connection with fluid mechanics
35B35Stability of solutions of PDE
Full Text: DOI
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