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On the derivation of linear elasticity from atomistic models
A mathematical model relevant for weakening of chalk reservoirs due to chemical reactions
1.  International Research Institute of Stavanger (IRIS), Prof. Olav Hanssensvei 15, NO4068 Stavanger, Norway 
2.  University of Stavanger (UiS), 4036 Stavanger, Norway, Norway 
[1] 
Danielle Hilhorst, Hideki Murakawa. Singular limit analysis of a reactiondiffusion system with precipitation and dissolution in a porous medium. Networks & Heterogeneous Media, 2014, 9 (4) : 669682. doi: 10.3934/nhm.2014.9.669 
[2] 
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) : 10131020. doi: 10.3934/proc.2007.2007.1013 
[3] 
Cedric Galusinski, Mazen Saad. Watergas flow in porous media. Conference Publications, 2005, 2005 (Special) : 307316. doi: 10.3934/proc.2005.2005.307 
[4] 
Steinar Evje, Aksel Hiorth. A mathematical model for dynamic wettability alteration controlled by waterrock chemistry. Networks & Heterogeneous Media, 2010, 5 (2) : 217256. doi: 10.3934/nhm.2010.5.217 
[5] 
Igor Pažanin, Marcone C. Pereira. On the nonlinear convectiondiffusionreaction problem in a thin domain with a weak boundary absorption. Communications on Pure & Applied Analysis, 2018, 17 (2) : 579592. doi: 10.3934/cpaa.2018031 
[6] 
Brahim Amaziane, Leonid Pankratov, Andrey Piatnitski. The existence of weak solutions to immiscible compressible twophase flow in porous media: The case of fields with different rocktypes. Discrete & Continuous Dynamical Systems  B, 2013, 18 (5) : 12171251. doi: 10.3934/dcdsb.2013.18.1217 
[7] 
Ivan Gentil, Bogusław Zegarlinski. Asymptotic behaviour of reversible chemical reactiondiffusion equations. Kinetic & Related Models, 2010, 3 (3) : 427444. doi: 10.3934/krm.2010.3.427 
[8] 
Matthieu Alfaro, Thomas Giletti. Varying the direction of propagation in reactiondiffusion equations in periodic media. Networks & Heterogeneous Media, 2016, 11 (3) : 369393. doi: 10.3934/nhm.2016001 
[9] 
Clément Cancès. On the effects of discontinuous capillarities for immiscible twophase flows in porous media made of several rocktypes. Networks & Heterogeneous Media, 2010, 5 (3) : 635647. doi: 10.3934/nhm.2010.5.635 
[10] 
Cédric Galusinski, Mazen Saad. A nonlinear degenerate system modelling watergas flows in porous media. Discrete & Continuous Dynamical Systems  B, 2008, 9 (2) : 281308. doi: 10.3934/dcdsb.2008.9.281 
[11] 
Jifa Jiang, Junping Shi. Dynamics of a reactiondiffusion system of autocatalytic chemical reaction. Discrete & Continuous Dynamical Systems  A, 2008, 21 (1) : 245258. doi: 10.3934/dcds.2008.21.245 
[12] 
Ting Zhang. The modeling error of well treatment for unsteady flow in porous media. Discrete & Continuous Dynamical Systems  B, 2015, 20 (7) : 21712185. doi: 10.3934/dcdsb.2015.20.2171 
[13] 
Patrick De Kepper, István Szalai. An effective design method to produce stationary chemical reactiondiffusion patterns. Communications on Pure & Applied Analysis, 2012, 11 (1) : 189207. doi: 10.3934/cpaa.2012.11.189 
[14] 
Petr Knobloch. Error estimates for a nonlinear local projection stabilization of transient convectiondiffusionreaction equations. Discrete & Continuous Dynamical Systems  S, 2015, 8 (5) : 901911. doi: 10.3934/dcdss.2015.8.901 
[15] 
Qiang Du, Zhan Huang, Richard B. Lehoucq. Nonlocal convectiondiffusion volumeconstrained problems and jump processes. Discrete & Continuous Dynamical Systems  B, 2014, 19 (2) : 373389. doi: 10.3934/dcdsb.2014.19.373 
[16] 
ZhenHui Bu, ZhiCheng Wang. Curved fronts of monostable reactionadvectiondiffusion equations in spacetime periodic media. Communications on Pure & Applied Analysis, 2016, 15 (1) : 139160. doi: 10.3934/cpaa.2016.15.139 
[17] 
Klemens Fellner, Wolfang Prager, Bao Q. Tang. The entropy method for reactiondiffusion systems without detailed balance: First order chemical reaction networks. Kinetic & Related Models, 2017, 10 (4) : 10551087. doi: 10.3934/krm.2017042 
[18] 
Youcef Amirat, Laurent Chupin, Rachid Touzani. Weak solutions to the equations of stationary magnetohydrodynamic flows in porous media. Communications on Pure & Applied Analysis, 2014, 13 (6) : 24452464. doi: 10.3934/cpaa.2014.13.2445 
[19] 
Matthias Erbar, Jan Maas. Gradient flow structures for discrete porous medium equations. Discrete & Continuous Dynamical Systems  A, 2014, 34 (4) : 13551374. doi: 10.3934/dcds.2014.34.1355 
[20] 
Xueying Wang, Drew Posny, Jin Wang. A reactionconvectiondiffusion model for cholera spatial dynamics. Discrete & Continuous Dynamical Systems  B, 2016, 21 (8) : 27852809. doi: 10.3934/dcdsb.2016073 
2017 Impact Factor: 1.187
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