coupled partial differential equation (pde)

Hi everyone! I have to solve the following system of two coupled partial differential equations:

dY/dt = a + b(Z-Y) + R (d^2 Y / dx^2)

dZ/dt = c(Y-Z) + T (d^2 Z / dx^2)

where Y,Z are my unknown functions, t is the time and x the space.

Unfortunately I don't know how to do... can someone give me some suggestions?

Thanks a lot in advance for all your support!

Pinco