American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Periodic orbits of tritrophic slow-fast system and double homoclinic bifurcations
  • PROC Home
  • This Issue
  • Next Article
    The changes of air gap in inductive engines as vibration indicator aided by mathematical model and artificial neural network
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
[1]

Yejuan Wang, Lin Yang. Global exponential attraction for multi-valued semidynamical systems with application to delay differential equations without uniqueness. Discrete and Continuous Dynamical Systems - B, 2019, 24 (4) : 1961-1987. doi: 10.3934/dcdsb.2018257
[2]

Zhiming Liu, Zhijian Yang. Global attractor of multi-valued operators with applications to a strongly damped nonlinear wave equation without uniqueness. Discrete and Continuous Dynamical Systems - B, 2020, 25 (1) : 223-240. doi: 10.3934/dcdsb.2019179
[3]

Siegfried Carl, Christoph Tietz. Quasilinear elliptic equations with measures and multi-valued lower order terms. Discrete and Continuous Dynamical Systems - S, 2018, 11 (2) : 193-212. doi: 10.3934/dcdss.2018012
[4]

Jingyu Wang, Yejuan Wang, Tomás Caraballo. Multi-valued random dynamics of stochastic wave equations with infinite delays. Discrete and Continuous Dynamical Systems - B, 2022  doi: 10.3934/dcdsb.2021310
[5]

Limei Dai. Multi-valued solutions to a class of parabolic Monge-Ampère equations. Communications on Pure and Applied Analysis, 2014, 13 (3) : 1061-1074. doi: 10.3934/cpaa.2014.13.1061
[6]

Yangrong Li, Renhai Wang, Lianbing She. Backward controllability of pullback trajectory attractors with applications to multi-valued Jeffreys-Oldroyd equations. Evolution Equations and Control Theory, 2018, 7 (4) : 617-637. doi: 10.3934/eect.2018030
[7]

Ting Li. Pullback attractors for asymptotically upper semicompact non-autonomous multi-valued semiflows. Communications on Pure and Applied Analysis, 2007, 6 (1) : 279-285. doi: 10.3934/cpaa.2007.6.279
[8]

Yejuan Wang, Peter E. Kloeden. The uniform attractor of a multi-valued process generated by reaction-diffusion delay equations on an unbounded domain. Discrete and Continuous Dynamical Systems, 2014, 34 (10) : 4343-4370. doi: 10.3934/dcds.2014.34.4343
[9]

Dalila Azzam-Laouir, Warda Belhoula, Charles Castaing, M. D. P. Monteiro Marques. Multi-valued perturbation to evolution problems involving time dependent maximal monotone operators. Evolution Equations and Control Theory, 2020, 9 (1) : 219-254. doi: 10.3934/eect.2020004
[10]

Yejuan Wang. On the upper semicontinuity of pullback attractors for multi-valued noncompact random dynamical systems. Discrete and Continuous Dynamical Systems - B, 2016, 21 (10) : 3669-3708. doi: 10.3934/dcdsb.2016116
[11]

Yejuan Wang, Tomás Caraballo. Morse decomposition for gradient-like multi-valued autonomous and nonautonomous dynamical systems. Discrete and Continuous Dynamical Systems - S, 2020, 13 (8) : 2303-2326. doi: 10.3934/dcdss.2020092
[12]

Peter Giesl. On a matrix-valued PDE characterizing a contraction metric for a periodic orbit. Discrete and Continuous Dynamical Systems - B, 2021, 26 (9) : 4839-4865. doi: 10.3934/dcdsb.2020315
[13]

Jiying Liu, Jubo Zhu, Fengxia Yan, Zenghui Zhang. Compressive sampling and $l_1$ minimization for SAR imaging with low sampling rate. Inverse Problems and Imaging, 2013, 7 (4) : 1295-1305. doi: 10.3934/ipi.2013.7.1295
[14]

Zhongwei Tang, Huafei Xie. Multi-spikes solutions for a system of coupled elliptic equations with quadratic nonlinearity. Communications on Pure and Applied Analysis, 2020, 19 (1) : 311-328. doi: 10.3934/cpaa.2020017
[15]

Ludovic Dan Lemle. $L^1(R^d,dx)$-uniqueness of weak solutions for the Fokker-Planck equation associated with a class of Dirichlet operators. Electronic Research Announcements, 2008, 15: 65-70. doi: 10.3934/era.2008.15.65
[16]

Yu Liu, Ting Zhang. On weak (measure-valued)-strong uniqueness for compressible MHD system with non-monotone pressure law. Discrete and Continuous Dynamical Systems - B, 2022  doi: 10.3934/dcdsb.2021307
[17]

María Anguiano, Tomás Caraballo, José Real, José Valero. Pullback attractors for reaction-diffusion equations in some unbounded domains with an $H^{-1}$-valued non-autonomous forcing term and without uniqueness of solutions. Discrete and Continuous Dynamical Systems - B, 2010, 14 (2) : 307-326. doi: 10.3934/dcdsb.2010.14.307
[18]

Long Hu, Tatsien Li, Bopeng Rao. Exact boundary synchronization for a coupled system of 1-D wave equations with coupled boundary conditions of dissipative type. Communications on Pure and Applied Analysis, 2014, 13 (2) : 881-901. doi: 10.3934/cpaa.2014.13.881
[19]

Shitao Liu, Roberto Triggiani. Determining damping and potential coefficients of an inverse problem for a system of two coupled hyperbolic equations. Part I: Global uniqueness. Conference Publications, 2011, 2011 (Special) : 1001-1014. doi: 10.3934/proc.2011.2011.1001
[20]

Yichen Zhang, Meiqiang Feng. A coupled $ p $-Laplacian elliptic system: Existence, uniqueness and asymptotic behavior. Electronic Research Archive, 2020, 28 (4) : 1419-1438. doi: 10.3934/era.2020075

 Impact Factor: 

Tools

Metrics

  • PDF downloads (48)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy