A hyperbolic “diffusion equation” taking a finite collision frequency into account

Using Bourret's approximation the effect of a finite correlation time τc of the velocity on the averaged displacement of a Brownian moving particle is investigated. It turns out that in a rather general special case the usual parabolic diffusion equation is replaced by a hyperbolic one. Both, this equation and its solution, approach the well-known parabolic result in the limit τc → 0.