How to solve coupled nonlinear 3-dimensional parabolic pde (x,y,t) in Matlab

Hi, I have a problem in solving nonlinear parabolic pde of following form. (consider u_x as differentiation of u w.r.t. x)

U(1)_t = a1(U(1),x)*U(2)_t + b1(U(1),x,U(3)) = ( D1(x,U(1))*U(1)_x )_x + c1( U(1), U(3))*U(1)_x ---(1)

and its coupled equation

U(3)_t = a2(U(1),U(3))*U(2)_t + b2(U(1),x,U(3)) = ( D3*U(3)_x )_x ---(2)

as you can see U(1), U(2), U(3) are there with only two PDE. That is because U(2) is not function of x and has its own pde as

U(2)_t = (1/r)( D2(U(2))*U(2)_r )_r ---(3)

Now (3) is standalone solvable. I solved it with pdepe in MATLAB. Now I need to put value of U(2)_t in (1)&(2) then solve them, which I couldn't do in pdepe.

So this is my question. Is there any way that after solving (3), value of U(2)_t could be imported in (1)&(2) and solve them simultaneously. Alternatively, is there any way that I can incoporate (3) directly in differential form in (1)&(2) and solve resulting coupled system in MATLAB. Thanks in Advance.