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Solvability of nonlinear evolution equations generated by subdifferentials and perturbations
Upscaling of reactive flows in domains with moving oscillating boundaries
1. | CASA, Technische Universiteit Eindhoven, Eindhoven, Netherlands, Netherlands |
2. | Department Mathematik, Chair of Applied Mathematics 1, Martensstr. 3, 91058 Erlangen, Germany |
References:
[1] |
G. Allaire and M. Amar, Boundary layer tails in periodic homogenization, ESAIM Control Optim. Calc. Var., 4 (1999), 209-243 (electronic).
doi: 10.1051/cocv:1999110. |
[2] |
J. M. Arrieta and S. M. Bruschi, Very rapidly varying boundaries in equations with nonlinear boundary conditions. The case of a non uniformly Lipschitz deformation, Discrete Contin. Dyn. Syst. Ser. B, 14 (2010), 327-351.
doi: 10.3934/dcdsb.2010.14.327. |
[3] |
J. M. Arrieta and M. C. Pereira, Homogenization in a thin domain with an oscillatory boundary, J. Math. Pures Appl. (9), 96 (2011), 29-57.
doi: 10.1016/j.matpur.2011.02.003. |
[4] |
K. Baber, K. Mosthaf, B. Flemisch, R. Helmig, S. Müthing and B. Wohlmuth, Numerical scheme for coupling two-phase compositional porous-media flow and one-phase compositional free flow, IMA J. Appl. Math., 77 (2012), 887-909.
doi: 10.1093/imamat/hxs048. |
[5] |
J. Bogers, K. Kumar, P. H. L. Notten, J. F. M. Oudenhoven and I. S. Pop, A multiscale domain decomposition approach for chemical vapor deposition, J. Comput. Appl. Math., 246 (2013), 65-73.
doi: 10.1016/j.cam.2012.10.018. |
[6] |
G. A. Chechkin, A. Friedman and A. L. Piatnitski, The boundary-value problem in domains with very rapidly oscillating boundary, J. Math. Anal. Appl., 231 (1999), 213-234.
doi: 10.1006/jmaa.1998.6226. |
[7] |
J. Donea, A. Huerta, J.-Ph. Ponthot and A. Rodriguez-Ferran, Arbitrary Lagrangian-Eulerian methods, The Encyclopedia of Computational Mechanics, Wiley, 1 (2004), 413-437. |
[8] |
C. J. van Duijn and P. Knabner, Travelling wave behaviour of crystal dissolution in porous media flow, European J. Appl. Math., 8 (1997), 49-72. |
[9] |
C. J. van Duijn, A. Mikelic, C. Rosier and I. S. Pop, Effective dispersion equations for reactive flows with dominant peclet and damkohler numbers, Advances in Chemical Engineering, 34 (2008), 1-45. |
[10] |
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.
doi: 10.1515/crll.2004.2004.577.171. |
[11] |
A. Friedman and B. Hu, A non-stationary multi-scale oscillating free boundary for the Laplace and heat equations, J. Differential Equations, 137 (1997), 119-165.
doi: 10.1016/S0022-0396(06)80006-9. |
[12] |
A. Friedman, B. Hu and Y. Liu, A boundary value problem for the Poisson equation with multi-scale oscillating boundary, J. Differential Equations, 137 (1997), 54-93.
doi: 10.1006/jdeq.1997.3257. |
[13] |
M. K. Gobbert and C. A. Ringhofer, An asymptotic analysis for a model of chemical vapor deposition on a microstructured surface, SIAM J. Appl. Math., 58 (1998), 737-752 (electronic).
doi: 10.1137/S0036139999528467. |
[14] |
F. Golfier, B. D. Wood, L. Orgogozo, M. Quintard and M. Buès, Biofilms in porous media: Development of macroscopic transport equations via volume averaging with closure for local mass equilibrium, Adv. Water Res., 32 (2009), 463-485.
doi: 10.1016/j.advwatres.2008.11.012. |
[15] |
E. Hairer and G. Wanner, On the instability of the BDF formulas, SIAM J. Numer. Anal., 20 (1983), 1206-1209.
doi: 10.1137/0720090. |
[16] |
, COMSOL Inc., http://www.comsol.com. |
[17] |
W. Jäger and A. Mikelić, On the boundary conditions at the contact interface between a porous medium and a free fluid, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 23 (1996), 403-465. |
[18] |
W. Jäger and A. Mikelić, On the interface boundary condition of Beavers, Joseph, and Saffman, SIAM J. Appl. Math., 60 (2000), 1111-1127 (electronic).
doi: 10.1137/S003613999833678X. |
[19] |
W. Jäger and A. Mikelić, On the roughness-induced effective boundary conditions for an incompressible viscous flow, J. Differential Equations, 170 (2001), 96-122.
doi: 10.1006/jdeq.2000.3814. |
[20] |
K. Kumar, M. van Helvoort and I. S. Pop, Rigorous upscaling of rough boundaries for reactive flows, CASA Report 12-37, 2012. |
[21] |
K. Kumar, T. L. van Noorden and I. S. Pop, Effective dispersion equations for reactive flows involving free boundaries at the microscale, Multiscale Model. Simul., 9 (2011), 29-58.
doi: 10.1137/100804553. |
[22] |
, MATLAB, http://www.mathworks.com. |
[23] |
K. Mosthaf, K. Baber, B. Flemisch, R. Helmig, A. Leijnse, I. Rybak and B. Wohlmuth, A coupling concept for two-phase compositional porous-medium and single-phase compositional free flow, Water Resour. Res., 47 (2011), W10522.
doi: 10.1029/2011WR010685. |
[24] |
N. Neuss, M. Neuss-Radu and A. Mikelić, Effective laws for the Poisson equation on domains with curved oscillating boundaries, Appl. Anal., 85 (2006), 479-502.
doi: 10.1080/00036810500340476. |
[25] |
T. L. van Noorden, Crystal precipitation and dissolution in a porous medium: Effective equations and numerical experiments, Multiscale Model. Simul., 7 (2008), 1220-1236.
doi: 10.1137/080722096. |
[26] |
T. L. van Noorden, Crystal precipitation and dissolution in a thin strip, European J. Appl. Math., 20 (2009), 69-91.
doi: 10.1017/S0956792508007651. |
[27] |
T. L. van Noorden, I. S. Pop, A. Ebigbo and R. Helmig, An upscaled model for biofilm growth in a thin strip, Water Resour. Res., 46 (2010), W06505. |
[28] |
P. H. L. Notten, F. Roozeboom, R. A. H. Niessen and L. Baggetto, 3-d integrated all-solid-state rechargeable batteries, Advanced Materials, 19 (2007), 4564-4567.
doi: 10.1002/adma.200702398. |
[29] |
J. F. M. Oudenhoven, L. Bagetto and P. H. L. Notten, All-solid-state lithium-ion microbatteries: A review of vaious three-dimensional concepts, Advanced Energy Materials, 1 (2011), 10-33. |
[30] |
J. F. M. Oudenhoven, T. van Dongen, R. A. H. Niessen, M. H. J. M. de Croon and P. H. L. Notten, Low-pressure chemical vapor deposition of licoo2 thin films: A systematic investigation of the deposition parameters, Journal of the Electrochemical Society, 156 (2009), D159-D174. |
show all references
References:
[1] |
G. Allaire and M. Amar, Boundary layer tails in periodic homogenization, ESAIM Control Optim. Calc. Var., 4 (1999), 209-243 (electronic).
doi: 10.1051/cocv:1999110. |
[2] |
J. M. Arrieta and S. M. Bruschi, Very rapidly varying boundaries in equations with nonlinear boundary conditions. The case of a non uniformly Lipschitz deformation, Discrete Contin. Dyn. Syst. Ser. B, 14 (2010), 327-351.
doi: 10.3934/dcdsb.2010.14.327. |
[3] |
J. M. Arrieta and M. C. Pereira, Homogenization in a thin domain with an oscillatory boundary, J. Math. Pures Appl. (9), 96 (2011), 29-57.
doi: 10.1016/j.matpur.2011.02.003. |
[4] |
K. Baber, K. Mosthaf, B. Flemisch, R. Helmig, S. Müthing and B. Wohlmuth, Numerical scheme for coupling two-phase compositional porous-media flow and one-phase compositional free flow, IMA J. Appl. Math., 77 (2012), 887-909.
doi: 10.1093/imamat/hxs048. |
[5] |
J. Bogers, K. Kumar, P. H. L. Notten, J. F. M. Oudenhoven and I. S. Pop, A multiscale domain decomposition approach for chemical vapor deposition, J. Comput. Appl. Math., 246 (2013), 65-73.
doi: 10.1016/j.cam.2012.10.018. |
[6] |
G. A. Chechkin, A. Friedman and A. L. Piatnitski, The boundary-value problem in domains with very rapidly oscillating boundary, J. Math. Anal. Appl., 231 (1999), 213-234.
doi: 10.1006/jmaa.1998.6226. |
[7] |
J. Donea, A. Huerta, J.-Ph. Ponthot and A. Rodriguez-Ferran, Arbitrary Lagrangian-Eulerian methods, The Encyclopedia of Computational Mechanics, Wiley, 1 (2004), 413-437. |
[8] |
C. J. van Duijn and P. Knabner, Travelling wave behaviour of crystal dissolution in porous media flow, European J. Appl. Math., 8 (1997), 49-72. |
[9] |
C. J. van Duijn, A. Mikelic, C. Rosier and I. S. Pop, Effective dispersion equations for reactive flows with dominant peclet and damkohler numbers, Advances in Chemical Engineering, 34 (2008), 1-45. |
[10] |
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.
doi: 10.1515/crll.2004.2004.577.171. |
[11] |
A. Friedman and B. Hu, A non-stationary multi-scale oscillating free boundary for the Laplace and heat equations, J. Differential Equations, 137 (1997), 119-165.
doi: 10.1016/S0022-0396(06)80006-9. |
[12] |
A. Friedman, B. Hu and Y. Liu, A boundary value problem for the Poisson equation with multi-scale oscillating boundary, J. Differential Equations, 137 (1997), 54-93.
doi: 10.1006/jdeq.1997.3257. |
[13] |
M. K. Gobbert and C. A. Ringhofer, An asymptotic analysis for a model of chemical vapor deposition on a microstructured surface, SIAM J. Appl. Math., 58 (1998), 737-752 (electronic).
doi: 10.1137/S0036139999528467. |
[14] |
F. Golfier, B. D. Wood, L. Orgogozo, M. Quintard and M. Buès, Biofilms in porous media: Development of macroscopic transport equations via volume averaging with closure for local mass equilibrium, Adv. Water Res., 32 (2009), 463-485.
doi: 10.1016/j.advwatres.2008.11.012. |
[15] |
E. Hairer and G. Wanner, On the instability of the BDF formulas, SIAM J. Numer. Anal., 20 (1983), 1206-1209.
doi: 10.1137/0720090. |
[16] |
, COMSOL Inc., http://www.comsol.com. |
[17] |
W. Jäger and A. Mikelić, On the boundary conditions at the contact interface between a porous medium and a free fluid, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 23 (1996), 403-465. |
[18] |
W. Jäger and A. Mikelić, On the interface boundary condition of Beavers, Joseph, and Saffman, SIAM J. Appl. Math., 60 (2000), 1111-1127 (electronic).
doi: 10.1137/S003613999833678X. |
[19] |
W. Jäger and A. Mikelić, On the roughness-induced effective boundary conditions for an incompressible viscous flow, J. Differential Equations, 170 (2001), 96-122.
doi: 10.1006/jdeq.2000.3814. |
[20] |
K. Kumar, M. van Helvoort and I. S. Pop, Rigorous upscaling of rough boundaries for reactive flows, CASA Report 12-37, 2012. |
[21] |
K. Kumar, T. L. van Noorden and I. S. Pop, Effective dispersion equations for reactive flows involving free boundaries at the microscale, Multiscale Model. Simul., 9 (2011), 29-58.
doi: 10.1137/100804553. |
[22] |
, MATLAB, http://www.mathworks.com. |
[23] |
K. Mosthaf, K. Baber, B. Flemisch, R. Helmig, A. Leijnse, I. Rybak and B. Wohlmuth, A coupling concept for two-phase compositional porous-medium and single-phase compositional free flow, Water Resour. Res., 47 (2011), W10522.
doi: 10.1029/2011WR010685. |
[24] |
N. Neuss, M. Neuss-Radu and A. Mikelić, Effective laws for the Poisson equation on domains with curved oscillating boundaries, Appl. Anal., 85 (2006), 479-502.
doi: 10.1080/00036810500340476. |
[25] |
T. L. van Noorden, Crystal precipitation and dissolution in a porous medium: Effective equations and numerical experiments, Multiscale Model. Simul., 7 (2008), 1220-1236.
doi: 10.1137/080722096. |
[26] |
T. L. van Noorden, Crystal precipitation and dissolution in a thin strip, European J. Appl. Math., 20 (2009), 69-91.
doi: 10.1017/S0956792508007651. |
[27] |
T. L. van Noorden, I. S. Pop, A. Ebigbo and R. Helmig, An upscaled model for biofilm growth in a thin strip, Water Resour. Res., 46 (2010), W06505. |
[28] |
P. H. L. Notten, F. Roozeboom, R. A. H. Niessen and L. Baggetto, 3-d integrated all-solid-state rechargeable batteries, Advanced Materials, 19 (2007), 4564-4567.
doi: 10.1002/adma.200702398. |
[29] |
J. F. M. Oudenhoven, L. Bagetto and P. H. L. Notten, All-solid-state lithium-ion microbatteries: A review of vaious three-dimensional concepts, Advanced Energy Materials, 1 (2011), 10-33. |
[30] |
J. F. M. Oudenhoven, T. van Dongen, R. A. H. Niessen, M. H. J. M. de Croon and P. H. L. Notten, Low-pressure chemical vapor deposition of licoo2 thin films: A systematic investigation of the deposition parameters, Journal of the Electrochemical Society, 156 (2009), D159-D174. |
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