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

T. L. van Noorden; I. S. Pop; M. Röger

doi:10.3934/proc.2007.2007.1013

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2007, Volume 2007: 1013-1020. Doi: 10.3934/proc.2007.2007.1013 open access

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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
2.
Max Planck Institute for Mathematics in the Sciences, Inselstr. 22, D-04103 Leipzig

Received: August 31, 2006

Revised: July 31, 2007

Published: August 2007

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Abstract

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.

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Mathematics Subject Classification: Primary: 35R70, 80A32; Secondary: 35K60, 76S05.

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