Template:Shallow depth one dimension

[math]\displaystyle{ \partial_t^2 \zeta = \partial_x \left(h(x) \partial_x \zeta \right). }[/math]

subject to the boundary conditions

[math]\displaystyle{ \zeta_{t=0} = \zeta_0\,\,\,{\rm and}\,\,\, \partial_t\zeta_{t=0} = \partial_t\zeta_0 }[/math]