The paper is concerned with an initial-boundary-value problem of the sixth order Boussinesq equation posed on a quarter plane with non-homogeneous boundary conditions:
where
$H^s(\mathbb{R}^+)× H^{s-1}(\mathbb{R}^+)$
and the naturally compatible boundary data
$\mbox{ $h_1∈ H_{loc}^{\frac{s+1}{3}}(\mathbb{R}^+)$, $h_2∈ H_{loc}^{\frac{s-1}{3}}(\mathbb{R}^+) \text{and}\,\,\, h_3∈ H_{loc}^{\frac{s-3}{3}}(\mathbb{R}^+)$}$
with optimal regularity.
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