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.

Degenerate parabolic equations (msc 35K65), Nonlinear initial value problems for linear parabolic equations (msc 35K60), Asymptotic behavior of solutions (msc 35B40)
Modelling, Analysis and Simulation [MAS]

van Duijn, C.J, Guerra, I.A, & Peletier, M.A. (2000). Asymptotic results for injection of reactive solutes from a three-dimensional well. Modelling, Analysis and Simulation [MAS]. CWI.