How to treat a infinite domain?

Dear all,

I want to simulate a diffusion-controlled problem in a semi-infinite domain. Assume that x>=0 is the semi-infinite domain, having initially a uniform substance concentration phi=phi0 for x >0 and zero substance concentration phi=0 for x =0. I want to know how the substance diffuse into the position x=0 from x>0, so I have to choose a computational domain with finite size. For example, x is chosen from 0 to 500 lattice grids. Anyone can tell me how to impose a boundary condition at boundary x = 500, which can well simulate the diffusion process? Many thanks.