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Homogenization of a poro-elasticity model coupled with diffusive transport and a first order reaction for concrete
1. | Centre for Industrial Mathematics, FB 3, University of Bremen, Bibliotheksstr., 28201, Bremen, Germany, Germany |
References:
[1] |
A. Ainouz, Homogenization of a double porosity model in deformable media,, Electronic Journal of Differential Equations, 90 (2013), 1.
|
[2] |
G. Allaire, Homogenization and two-scale convergence,, SIAM Journal on Mathematical Analysis, 23 (1992), 1482.
doi: 10.1137/0523084. |
[3] |
G. Allaire, A. Damlamian and U. Hornung, Two-scale convergence on periodic surfaces and applications,, in Proceedings of the International Conference on Mathematical Modelling of Flow through Porous Media, (1995), 15. Google Scholar |
[4] |
T. Arbogast, J. Douglas and U. Hornung, Derivation of the double porosity model of single phase flow via homogenization theory,, SIAM Journal on Mathematical Analysis, 21 (1990), 823.
doi: 10.1137/0521046. |
[5] |
M. Biot, General theory of three-dimensional consolidation,, Journal of applied physics, 12 (1941), 155.
doi: 10.1063/1.1712886. |
[6] |
O. Coussy, Poromechanics,, 2nd edition, (2005).
doi: 10.1002/0470092718. |
[7] |
H. Deresiewicz and R. Skalak, On uniqueness in dynamic poroelasticity,, Bulletin of the Seismological Society of America, 53 (1963), 783. Google Scholar |
[8] |
M. Eden, Poroelasticity,, Master's thesis, (2014). Google Scholar |
[9] |
I. Graf, M. Peter and J. Sneyd, Homogenization of a nonlinear multiscale model of calcium dynamics in biological cells,, Journal of Mathematical Analysis and Applications, 419 (2014), 28.
doi: 10.1016/j.jmaa.2014.04.037. |
[10] |
U. Hornung and W. Jäger, Diffusion, convection, adsorption, and reaction of chemicals in porous media,, Journal of differential equations, 92 (1991), 199.
doi: 10.1016/0022-0396(91)90047-D. |
[11] |
A. Meirmanov and R. Zimin, Compactness result for periodic structures and its application to the homogenization of a diffusion-convection equation,, Electronic Journal of Differential Equations, 115 (2011), 1.
|
[12] |
S. Monsurrò, Homogenization of a two-component composite with interfacial thermal barrier,, Adv. Math. Sci. Appl., 13 (2003), 43.
|
[13] |
G. Nguetseng, A general convergence result for a functional related to the theory of homogenization,, SIAM Journal on Mathematical Analysis, 20 (1989), 608.
doi: 10.1137/0520043. |
[14] |
G. Pavliotis and A. Stuart, Multiscale Methods: Averaging and Homogenization (Texts in Applied Mathematics),, Springer, (2008).
|
[15] |
M. Peter and M. Böhm, Different choices of scaling in homogenization of diffusion and interfacial exchange in a porous medium,, Mathematical Methods in the Applied Sciences, 31 (2008), 1257.
doi: 10.1002/mma.966. |
[16] |
R. Showalter, Distributed microstructure models of porous media,, in Flow in porous media, 114 (1993), 155.
|
[17] |
R. Showalter, Hilbert Space Methods in Partial Differential Equations (Dover Books on Mathematics),, Dover Publications, (2010). Google Scholar |
[18] |
R. Showalter and B. Momken, Single-phase Flow in Composite Poro-elastic Media,, Technical report, (2002). Google Scholar |
[19] |
L. Tartar, The General Theory of Homogenization: A Personalized Introduction (Lecture Notes of the Unione Matematica Italiana),, 2010th edition, (2009).
doi: 10.1007/978-3-642-05195-1. |
[20] |
F.-J. Ulm, G. Constantinides and F. Heukamp, Is concrete a poromechanics materials? A multiscale investigation of poroelastic properties,, Materials and Structures, 37 (2004), 43. Google Scholar |
[21] |
E. Zeidler, Nonlinear Functional Analysis and Its Applications: II/ B: Nonlinear Monotone Operators,, Translated from the German by the author and Leo F. Boron. Springer-Verlag, (1990).
doi: 10.1007/978-1-4612-0985-0. |
show all references
References:
[1] |
A. Ainouz, Homogenization of a double porosity model in deformable media,, Electronic Journal of Differential Equations, 90 (2013), 1.
|
[2] |
G. Allaire, Homogenization and two-scale convergence,, SIAM Journal on Mathematical Analysis, 23 (1992), 1482.
doi: 10.1137/0523084. |
[3] |
G. Allaire, A. Damlamian and U. Hornung, Two-scale convergence on periodic surfaces and applications,, in Proceedings of the International Conference on Mathematical Modelling of Flow through Porous Media, (1995), 15. Google Scholar |
[4] |
T. Arbogast, J. Douglas and U. Hornung, Derivation of the double porosity model of single phase flow via homogenization theory,, SIAM Journal on Mathematical Analysis, 21 (1990), 823.
doi: 10.1137/0521046. |
[5] |
M. Biot, General theory of three-dimensional consolidation,, Journal of applied physics, 12 (1941), 155.
doi: 10.1063/1.1712886. |
[6] |
O. Coussy, Poromechanics,, 2nd edition, (2005).
doi: 10.1002/0470092718. |
[7] |
H. Deresiewicz and R. Skalak, On uniqueness in dynamic poroelasticity,, Bulletin of the Seismological Society of America, 53 (1963), 783. Google Scholar |
[8] |
M. Eden, Poroelasticity,, Master's thesis, (2014). Google Scholar |
[9] |
I. Graf, M. Peter and J. Sneyd, Homogenization of a nonlinear multiscale model of calcium dynamics in biological cells,, Journal of Mathematical Analysis and Applications, 419 (2014), 28.
doi: 10.1016/j.jmaa.2014.04.037. |
[10] |
U. Hornung and W. Jäger, Diffusion, convection, adsorption, and reaction of chemicals in porous media,, Journal of differential equations, 92 (1991), 199.
doi: 10.1016/0022-0396(91)90047-D. |
[11] |
A. Meirmanov and R. Zimin, Compactness result for periodic structures and its application to the homogenization of a diffusion-convection equation,, Electronic Journal of Differential Equations, 115 (2011), 1.
|
[12] |
S. Monsurrò, Homogenization of a two-component composite with interfacial thermal barrier,, Adv. Math. Sci. Appl., 13 (2003), 43.
|
[13] |
G. Nguetseng, A general convergence result for a functional related to the theory of homogenization,, SIAM Journal on Mathematical Analysis, 20 (1989), 608.
doi: 10.1137/0520043. |
[14] |
G. Pavliotis and A. Stuart, Multiscale Methods: Averaging and Homogenization (Texts in Applied Mathematics),, Springer, (2008).
|
[15] |
M. Peter and M. Böhm, Different choices of scaling in homogenization of diffusion and interfacial exchange in a porous medium,, Mathematical Methods in the Applied Sciences, 31 (2008), 1257.
doi: 10.1002/mma.966. |
[16] |
R. Showalter, Distributed microstructure models of porous media,, in Flow in porous media, 114 (1993), 155.
|
[17] |
R. Showalter, Hilbert Space Methods in Partial Differential Equations (Dover Books on Mathematics),, Dover Publications, (2010). Google Scholar |
[18] |
R. Showalter and B. Momken, Single-phase Flow in Composite Poro-elastic Media,, Technical report, (2002). Google Scholar |
[19] |
L. Tartar, The General Theory of Homogenization: A Personalized Introduction (Lecture Notes of the Unione Matematica Italiana),, 2010th edition, (2009).
doi: 10.1007/978-3-642-05195-1. |
[20] |
F.-J. Ulm, G. Constantinides and F. Heukamp, Is concrete a poromechanics materials? A multiscale investigation of poroelastic properties,, Materials and Structures, 37 (2004), 43. Google Scholar |
[21] |
E. Zeidler, Nonlinear Functional Analysis and Its Applications: II/ B: Nonlinear Monotone Operators,, Translated from the German by the author and Leo F. Boron. Springer-Verlag, (1990).
doi: 10.1007/978-1-4612-0985-0. |
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