  We investigate a simple inhomogeneous anisotropic cosmology (plane symmetric
$G_2$ model) filled with a tilted perfect fluid undergoing velocity diffusion
on a scalar field. Considered are two types of fluid: dust and radiation. We
solve the system of Einstein field equations and diffusion equations
numerically and demonstrate how the universe evolves towards its future
asymptotic state. Also, typical time scales of characteristic processes are
determined. The obtained results for dust- and radiation-filled cosmologies are
compared to each other and to those in the diffusionless case, giving a hint on
which effects can be the result of including diffusion in more complicated
models. For example, diffusion causes the accelerated expansion stage to arrive
at later times.
