I have a similar question (I think).
Can the pdepe tool solve coupled pde's?
The example on the link you sent has a vector of coefficients for the f function that depend on DuDx. Can I enter Du(1)Dx and Du(2)Dx? Below is the general form of the equations:
Thanks in advance!
d(u1)/dt = d/dx (d(u1)/dx - d(u2)/dx))
d(u2)/dt = d/dx (d(u2)/dx - d(u2)/dx))