Solving 2nd order hyperbolic PDE; Goursat problem

Hi All,

I'm in need of some help with understanding how to numerically solve a 1D 2nd order hyperbolic Goursat problem shown below. The issue that I can't seem to get around is the boundary condition of k(x,x)=-.5*integral(q(E)dE).

I have tried to set up solutions using both the pdetool and the hyperbolic() function, but don't understand how I would enter the k(x,x) boundary condition. I have even been constraining the problem to have q(x)=0 so that the boundary condition k(x,x)=0.

Thanks for the insight, Chris