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2007, 2007(Special): 1013-1020. doi: 10.3934/proc.2007.2007.1013

Crystal dissolution and precipitation in porous media: L$^1$-contraction and uniqueness

T. L. van Noorden 1, , I. S. Pop 1, and  M. Röger 2,

1. 

Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O.Box 513, 5600 MB Eindhoven, Netherlands, Netherlands
2. 

Max Planck Institute for Mathematics in the Sciences, Inselstr. 22, D-04103 Leipzig, Germany

Received  September 2006 Revised  August 2007 Published  September 2007

In this note we continue the analysis of the pore-scale model for crystal dissolution and precipitation in porous media proposed in [C. J. van Duijn and I. S. Pop, Crystal dissolution and precipitation in porous media: pore scale analysis, J. Reine Angew. Math. 577 (2004), 171–211]. There the existence of weak solutions was shown. We prove an L1-contraction property of the pore-scale model. As a direct consequence we obtain the uniqueness of (weak) solutions.
Keywords: Coupled system, L^1 contraction, multi-valued rate, uniqueness..
Mathematics Subject Classification: Primary: 35R70, 80A32; Secondary: 35K60, 76S0.
Citation: T. L. van Noorden, I. S. Pop, M. Röger. Crystal dissolution and precipitation in porous media: L$^1$-contraction and uniqueness. Conference Publications, 2007, 2007 (Special) : 1013-1020. doi: 10.3934/proc.2007.2007.1013
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