Given known functions $a(x,y)$ and $b(x,y)$, I have a linear, second-order, hyperbolic PDE for a surface $z(x,y)$. The PDE is of the form:  

$z\_{xx} - a^2 z\_{yy} + ab z\_x - b z\_y = 0$.

The PDE does not have $z\_{xy}$ term, $z$ term and constant term.

Along a closed boundary contour, it is known that both $z\_x$ and $z\_y$ approach infinity. But the limiting ratio $c(x,y) = {z\_y}/{z\_x}$ is known at the boundary.

The boundary conditions are somewhat unusual, but they arise naturally in my application. 

Can the above PDE be solved with such BCs? If I need to specify additional conditions, what should they be? (I suppose at the least I will need to specify the value of z at some points in the domain.)