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

Abstract

In this paper we consider some asymptotic aspects related to the profile of a reactive solute, which is injected from a well (radius ε 0) into a three-dimensional porous medium. We present a convergence result for ε ↓ 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 C. J. van Duijn and M. A. Peletier (1996, J. Reine Angew. Math. 479, 77-98), where the two-dimensional case was treated. © 2001 Academic Press.