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

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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

Abstract
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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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