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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

 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.
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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