Boundary Conditions for a system of PDE

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Given a system of following PDEs:

$$ u_{x} + v_{y} + 3u-v=0 \\ u_{y} - w_{x}+uw=0 \\ v_{x}-w_{y}=0 $$

I found that the given system of equations is of mixed elliptic-hyperbolic type with the characteristics as $1, \frac{-1\pm \sqrt{3}i}{2}$
The goal is to find where initial conditions and boundary conditions should be prescribed on a rectangular domain.

Now the solution given to me is as shown here

Solution of Boundary Conditions

Can someone please help me in understanding how we arrived at this solution?