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

Pages: 1013 - 1020, Issue Special, September 2007

 Abstract        Full Text (180.0K)              

T. L. van Noorden - Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O.Box 513, 5600 MB Eindhoven, Netherlands (email)
I. S. Pop - Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O.Box 513, 5600 MB Eindhoven, Netherlands (email)
M. Röger - Max Planck Institute for Mathematics in the Sciences, Inselstr. 22, D-04103 Leipzig, Germany (email)

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.

Keywords:  Coupled system, multi-valued rate, L^1 contraction, uniqueness.
Mathematics Subject Classification:  Primary: 35R70, 80A32; Secondary: 35K60, 76S05.

Received: September 2006;      Revised: August 2007;      Published: September 2007.