Travelling wave behaviour of crystal dissolution in porous media flow.
- Knabner, Peter
- van Duijn, Cornelius J.
2010 Mathematics Subject Classification
- 35K65 35K57 35R35 35B30 76S05
- Degenerate parabolic equation, flow in porous media, travelling wave solutions, asymptotic analysis
In this paper we present a model for crystal dissolution in porous media and we analyse travelling wave solutions of the ensuing equations for a one-dimensional flow situation. We demonstrate the structure of the waves and we prove existence and uniqueness. The travelling wave description is characterized by a rate parameter k and a diffusion/dispersion parameter D. We investigate the limit processes as k → ∞ and
D → 0 and we obtain expressions for the rate of convergence. We also present some numerical results.