View source for Template:Standard linear wave scattering equations without body condition

<center><math>
\begin{align}
\Delta\phi &=0, &-h<z<0,\,\,\mathbf{x} \in \Omega \\
\partial_z\phi &= 0, &z=-h, \\
 \partial_z \phi  &= \alpha \phi, &z=0,\,\,\mathbf{x} \in \partial \Omega_{\mathrm{F}},
\end{align}
</math></center>


(note that the last expression can be obtained from combining the expressions:
<center><math>
\begin{align}
 \partial_z \phi  &= -\mathrm{i} \omega \zeta, &z=0,\,\,\mathbf{x} \in \partial \Omega_{\mathrm{F}}, \\
\mathrm{i} \omega \phi  &= g\zeta, &z=0,\,\,\mathbf{x} \in \partial \Omega_{\mathrm{F}},
\end{align}
</math></center>

where <math>\alpha = \omega^2/g \,</math>)