On two-scale convergence and periodic unfolding

Franců, Jan

doi:10.2478/v10127-011-0007-3

Abstract

Two-scale convergence is an important tool in homogenization theory. The contribution deals with various primary and adjoint (based on unfolding) approaches to the two-scale convergence and their pro-and-con.

References

[1] ALLAIRE, G.: Homogenization and two-scale convergence, SIAM J. Math. Anal. 23 (1992), 1482-1518.10.1137/0523084
Search in Google Scholar
[2] ARBOGAST, T.-DOUGLAS, J.-HORNUNG, U.: Derivation of the double porosity model of single phase flow via homogenization theory, SIAM J. Math. Anal. 21 (1990), 823-836.10.1137/0521046
Search in Google Scholar
[3] BENSOUSSAN, A.-LIONS, J. L.-PAPANICOLAOU, G.: Asymptotic Analysis for Periodic Structures, in: Stud. Math. Appl., Vol. 5, North-Holland, Amsterdam, 1978.
Search in Google Scholar
[4] CIORANESCU, D.-DAMLAMIAN, A.-GRISO, G.: Periodic unfolding and homogenization, C. R. Math. Acad. Sci. Paris 335 (2002), 99-104.10.1016/S1631-073X(02)02429-9
Search in Google Scholar
[5] CIORANESCU, D.-DAMLAMIAN, A.-GRISO, G.: The periodic unfolding method in homogenization, SIAM J. Math. Anal. 40 (2008), 1585-1620.10.1137/080713148
Search in Google Scholar
[6] DAMLAMIAN, A.: An elementary introduction to periodic unfolding, in: Proc. of the Narvic Conference (A. Damlamian et al.), Narvik, Norway, 2004, GAKUTO Internat. Ser. Math. Sci. Appl., Vol. 24, Gakk¯otosho, Tokyo, 2006, pp. 119-136.
Search in Google Scholar
[7] FRANC°U, J.: On two-scale convergence, in: Proc. of the 6th Math. Workshop, Faculty of Civil Engineering, Brno University of Technology, Brno, October 18, 2007, CD, 7 p.
Search in Google Scholar
[8] FRANC°U, J.: Modification of unfolding approach to two-scale convergence, Math. Bohem. 135 (2010), 403-412.10.21136/MB.2010.140831
Search in Google Scholar
[9] FRANC°U, J.-SVANSTEDT, N.: Some remarks on two-scale convergence and periodic unfolding, Appl. Math., 2011 (to appear).
Search in Google Scholar
[10] HOLMBOM, A.-SILFVER, J.-SVANSTEDT, N.-WELLANDER, N.: On two-scale convergence and related sequential compactness topics, Appl. Math. 51 (2006), 247-262.10.1007/s10492-006-0014-x
Search in Google Scholar
[11] LUKKASSEN, D.-NGUETSENG, G.-WALL, P.: Two-scale convergence, Int. J. Pure Appl. Math. 2 (2002), 35-86.
Search in Google Scholar
[12] MURAT, F.: Compacite par compensation, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 22 (1978), 489-507.
Search in Google Scholar
[13] NECHV´ATAL, L.: Alternative approach to the two-scale convergence, Appl. Math. 49 (2004), 97-110.10.1023/B:APOM.0000027218.04167.9b
Search in Google Scholar
[14] NGUETSENG, G.: A general convergence result for a functional related to the theory of homogenization, SIAM J. Math. Anal. 20 (1989), 608-623.10.1137/0520043
Search in Google Scholar
[15] NGUETSENG, G.-SVANSTEDT, N.: ∑-convergence. Banach J. Math. Anal. (to appear).
Search in Google Scholar

On two-scale convergence and periodic unfolding

Abstract

Paradigm

My account