Comptes Rendus
Homogenisation in domains with evolving microstructure
Comptes Rendus. Mécanique, Volume 335 (2007) no. 7, pp. 357-362.

We propose a method which accounts for an evolving microstructure in homogenisation problems. The concept of the method is quite general and can be applied to a number of different problems. It makes use of a transformation to a homogenisable substitute problem on a fixed periodic domain.

On propose une méthode pour inclure une évolution de la micro-structure en problème d'homogénéisation. L'idée de la méthode est assez générale et peut être employée pour une diversité de problèmes différents. Elle utilise la transformation d'un problème substitué homogénéisé dans un domaine fixe périodique.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2007.05.024
Keywords: Homogenization, Multiscale approach, Porous media, Reaction–diffusion, Interfacial exchange
Mot clés : Homogénéisation, Approche multiéchelle, Milieux poreux, Reaction et diffusion, Transport de masse à travers une surface de séparation

Malte A. Peter 1

1 Centre for Industrial Mathematics, FB 3, University of Bremen, Postfach 330 440, 28334 Bremen, Germany
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Malte A. Peter. Homogenisation in domains with evolving microstructure. Comptes Rendus. Mécanique, Volume 335 (2007) no. 7, pp. 357-362. doi : 10.1016/j.crme.2007.05.024. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2007.05.024/

[1] A. Bensoussan; J.L. Lions; G. Papanicolaou Asymptotic Analysis for Periodic Structures, North-Holland, 1978

[2] E. Sanchez-Palencia Non-Homogeneous Media and Vibration Theory, Springer, 1980

[3] D. Cioranescu; P. Donato An Introduction to Homogenization, Oxford University Press, 1999

[4] C. Truesdell; R.A. Toupin The classical field theories (S. Flügge, ed.), Handbuch der Physik III/1, Springer, 1960, pp. 226-793

[5] M.A. Peter, Coupled reaction–diffusion systems and evolving microstructure: mathematical modelling and homogenisation, PhD dissertation, University of Bremen, Germany, 2006. Also: Logos Verlag Berlin, 2007

[6] R.E. Showalter Monotone Operators in Banach Space and Nonlinear Partial Differential Equations, American Mathematical Society, 1997

[7] G. Nguetseng A general convergence result for a functional related to the theory of homogenization, SIAM J. Math. Anal., Volume 20 (1989) no. 3, pp. 608-629

[8] G. Allaire Homogenization and two-scale convergence, SIAM J. Math. Anal., Volume 23 (1992) no. 6, pp. 1482-1518

[9] S.A. Meier; M. Böhm A two-scale reaction–diffusion system with time-dependent microstructure, Proc. Appl. Math. Mech., Volume 6 (2006) no. 1, pp. 647-648

[10] T. Arbogast; J. Douglas; U. Hornung Derivation of the double porosity model of single phase flow via homogenization theory, SIAM J. Math. Anal., Volume 21 (1990) no. 4, pp. 823-836

[11] U. Hornung; W. Jäger Diffusion, convection, adsorption, and reaction of chemicals in porous media, J. Differential Equations, Volume 92 (1991), pp. 199-225

[12] (U. Hornung, ed.), Homogenization and Porous Media, Springer, 1997

[13] M.A. Peter, M. Böhm, Scalings in homogenisation of reaction, diffusion and interfacial exchange in a two-phase medium, in: Proc. Equadiff-11 (in press)

[14] U. Hornung Applications of the homogenization method to flow and transport in porous media, Beijing, China, 8–26 August 1988 (X. Shutie, ed.), World Scientific (1992), pp. 167-222

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