[1] G. Allaire:
Homogenization and two-scale convergence. SIAM J. Math. Anal. 23 (1992), 1482–1512.
MR 1185639 |
Zbl 0770.35005
[2] T. Arbogast, J. Douglas and U. Hornung:
Derivation of the double porosity model of single phase flow via homogenization theory. SIAM J. Math. Anal. 21 (1990), 823–836.
MR 1052874
[3] I. Babuška:
Homogenization approach in engineering. In: Lecture Notes in Economics and Mathematical Systems, M. Berkmann, H. P. Kunzi (eds.), Springer, Berlin, 1975, pp. 137–153.
MR 0478946
[4] I. Babuška: Mathematics of the verification and validation in computational engineering. In: Mathematical and Computer Modelling in Science and Engineering. Proc. Int. Conf. in Prague (January 2003), Czech Tech. Univ. Prague, 2003, pp. 5–12.
[5] J. Barták, J. Herrmann, V. Lovicar and O. Vejvoda:
Partial Differential Equations of Evolution. Ellis Horwood-SNTL, New York-Prague, 1991.
MR 1112789
[6] G. Bouchitté, I. Fragalà:
Homogenization of thin structures by two-scale method with respect to measures. SIAM J. Math. Anal. 32 (2001), 1198–1226.
MR 1856245
[7] D. Cioranescu, P. Donato:
An Introduction to Homogenization. Oxford University Press, Oxford, 1999.
MR 1765047
[8] J. Dalík, J. Svoboda and S. Šťastník: A model of moisture and temperature propagation. Preprint, Techn. Univ. Brno (Faculty of Civil Engineering), 2000.
[9] J. Franců:
Monotone operators. A survey directed to applications to differential equations. Appl. Math. 35 (1990), 257–301.
MR 1065003
[10] J. Fučík, A. Kufner: Nonlinear Differential Equations. Elsevier, Amsterdam, 1980.
[11] A. Holmbom:
Homogenization of parabolic equations. An alternative approach and some corrector-type results. Appl. Math. 42 (1997), 321–343.
MR 1467553 |
Zbl 0898.35008
[12] W. Jäger, J. Kačur:
Solution of porous medium type systems by linear approximation schemes. Numer. Math. 60 (1991), 407–427.
MR 1137200
[13] J. Kačur:
Method of Rothe in Evolution Equations. Teubner, Leipzig, 1985.
MR 0834176
[14] A. Kufner, O. John and S. Fučík:
Function Spaces. Academia, Prague, 1977.
MR 0482102
[15] M. L. Mascarenhas, A.-M. Toader:
Scale convergence in homogenization. Preprint, Univ. Lisboa, 2000.
MR 1841866
[16] A.-M. Matache, Ch. Schwab:
Two-scale finite element method for homogenization problems. Math. Model. Numer. Anal. 26 (2002), 537–572.
MR 1932304
[17] V. G. Maz’ya: Sobolev Spaces. Izdat. Leningradskogo universiteta, Leningrad (St. Petersburg), 1985. (Russian)
[18] G. Nguetseng:
A general convergence result for a functional related to the theory of homogenization. SIAM J. Math. Anal. 20 (1989), 608–623.
MR 0990867 |
Zbl 0688.35007
[19] K. Rektorys:
The Method of Discretization in Time. Reidel, Dordrecht, 1982.
Zbl 0522.65059
[20] E. Rothe:
Zweidimensionale parabolische Randwertaufgaben als Grenzfall eindimensionaler Randwertaufgaben. Math. Ann. 102 (1930), 650–670.
MR 1512599
[21] T. Roubíček:
Relaxation in Optimization Theory and Variational Calculus. Walter de Gruyter, Berlin, 1997.
MR 1458067
[22] K. Segeth: Rothe method and method of lines. A brief discussion. In: Mathematical and Computer Modelling in Science and Engineering. Proc. Int. Conf. in Prague (January 2003), Czech Tech. Univ. Prague, 2003, pp. 316–320.
[23] J. Svoboda, J. Vala: Micromodelling of creep in composites with perfect matrix / particle interfaces. Metallic Materials 36 (1998), 109–129.
[24] J. Vala: Two-scale convergence in nonlinear evolution problems. In: Programy a algoritmy numerické matematiky. Proc. 11$^{\text{th}}$ Summer School in Dolní Maxov (June 2002), Math. Inst. Acad. Sci. Czech Rep, to appear. (Czech)
[25] J. Vala: Method of discretization in time and two-scale convergence for nonlinear problems of engineering mechanics. Mathematical and Computer Modelling in Science and Engineering. Proc. Int. Conf. in Prague (January 2003), Czech Techn. Univ. Prague, 2003, pp. 359–363.
[26] J. Vala: Two-scale convergence with respect to measures in continuum mechanics. Equadiff, CD-ROM Proc. 10$^{\text{th}}$ Int. Conf. in Prague (August 2001), Charles University in Prague. To appear.
[27] J. Vala:
Two-scale limits in some nonlinear problems of engineering mechanics. Math. Comput. Simulation 61 (2003), 177–185.
MR 1983667