Conjugated PDES with ''pdepe'' function

Hey guys. I need to solve the PDE system attached in the jpeg file. I was looking at the pdepe function in MATLAB that can actually solve similar cases. However, in my case there are some derivatives of u1 inside the 2nd equation ( the equation corresponds to u2). I wrote it in matrix form as MATLAB suggests in order to solve with this function but I'm not sure it's possible to solve it in this way.

Can someone shed light on this problem and maybe guide me a little bit?

Thanks,

Roi