Asymptotic results for injection of reactive solutes from a three-dimensional well

In this paper we consider some asymptotic aspects related to the profile of a reactive solute, which is injected from a well (radius $epsilon >0$) into a three-dimensional porous medium. We present a convergence result for $epsilon downarrow 0$ as well as the large time behaviour. Regarding the latter we show that the solute profile evolves in a self-similar way towards a stationary distribution and we give an estimate for the rate of the convergence. This paper extends earlier work of {sc van Duijn & Peletier [5], where the two-dimensional case was treated.