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Existence and scattering of small solutions to a Boussinesq type equation of sixth order. (English) Zbl 1195.35229
Summary: We consider the existence and uniqueness of the global small solution as well as the small data scattering result to the Cauchy problem for a Boussinesq type equation of sixth order with the nonlinear term $f(u)$ behaving as $u^p$ $(p>1)$ as $u\to 0$ in $\Bbb R^n$, $n\ge 1$. The main method and techniques used in our paper are the Littlewood-Paley dyadic decomposition, the stationary phase estimate and some properties of Bessel functions.

MSC:
35L76Semilinear higher-order hyperbolic equations
35L30Higher order hyperbolic equations, initial value problems
35Q35PDEs in connection with fluid mechanics
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References:
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