Solutions for a diffusion equation with a backbone term

We investigate the diffusion equation. partial derivative(t)rho = D-y partial derivative(2)(y)rho + D-x partial derivative(2)(x)rho + (D) over bar (x)delta(y)partial derivative(mu)(x)rho subjected to the boundary conditions rho(+/-infinity, y; t) = 0 and rho(x, +/-infinity; t) = 0, and the initial condition rho(x, y; 0) = (rho) over cap (x, y). We obtain exact solutions in terms of the Green function approach and analyze the mean square displacement in the x and y directions. This analysis shows an anomalous spreading of the system which is characterized by different diffusive regimes connected to anomalous diffusion.