I am currently searching for a nice book to read about homogenization of pde's (elliptic, parabolic or hyperbolic). I have found this one https://books.google.gr/books?id=s_hrxBdCu44C&redir_esc=y but I think I could use another opinion.
Thank you in advance
Here are some useful books/lectures on homogenization theory:
[1] G. Allaire, Homogenization and two-scale convergence SIAM J. Math. Anal. 23.6 (1992) 1482-1518
[2] G. Allaire, Shape optimization by the homogenization method, Springer Verlag, New York (2001)
[3] G. Allaire, C. Conca, Bloch wave homogenization and spectral asymptotic analysis, J. Math. Pures et Appli. 77, pp.153-208 (1998)
[4] T. Arbogast, J. Douglas, U. Hornung, Derivation of the double porosity model of single phase flow via homogenization theory, SIAM J. Math. Anal., 21 (1990), pp. 823-836
[5] N. Bakhvalov, G. Panasenko, Homogenization: Averaging Processes in Periodic Media Kluwer, Dordrecht (1989)
[6] A. Bensoussan, J.L. Lions, G. Papanicolaou, Asymptotic Analysis for Periodic Structures North-Holland, Amsterdam (1978)
[7] A. Braides, Γ-convergence for beginners, Oxford Lecture Series in Mathematics and its Applications, 22, Oxford University Press, Oxford (2002)
[8] R. Christensen, Mechanics of composite materials, John Wiley, New York (1979)
[9] D. Cioranescu, A. Damlamian, G. Griso, Periodic unfolding and homogenization, C.R. Acad. Sci. Paris, Ser. 1, 335 (2002), pp. 99-104
[10] D. Cioranescu, A. Damlamian, and G. Griso, The periodic unfolding method in homogenization, SIAM J. Math. Anal. 40 (2008), no. 4, 1585-1620
[11] D. Cioranescu, P. Donato, An introduction to homogenization, Oxford Lecture Series in Mathematics and Applications 17, Oxford (1999)
[12] G. Dal Maso, An Introduction to Γ-Convergence Birkh¨auser, Boston (1993)
[13] G. Dal Maso, L. Modica, Nonlinear stochastic homogenization and ergodic theory Journal f¨ur die reine und angewandte Mathematik 368 (1986) 28-42
[14] E. De Giorgi, Sulla convergenza di alcune successioni di integrali del tipo dell’area Rendi Conti di Mat. 8 (1975) 277-294
[15] E. De Giorgi, G-operators and Γ-convergence Proceedings of the international congress of mathematicians (Warsazwa, August 1983), PWN Polish Scientific Publishers and North Holland (1984) 1175-1191
[16] E. De Giorgi, S. Spagnolo, Sulla convergenza degli integrali dell’energia per operatori ellittici del secondo ordine Boll. Un. Mat. It. 8 (1973) 391-411
[17] U. Hornung, Homogenization and porous media, Interdisciplinary Applied Mathematics Series, vol. 6, (Contributions from G. Allaire, M. Avellaneda, J.L. Auriault, A. Bourgeat, H. Ene, K. Golden, U. Hornung, A. Mikelic, R. Showalter), Springer Verlag (1997)
[18] S. Kozlov, Averaging of random operators Math. USSR Sbornik 37 (1980) 167-180
[19] M. Lenczner, Homog´en´eisation d’un circuit ´electrique, C.R. Acad. Sci. Paris, Ser. 2, 324 (1997), pp. 537-542
[20] J.L. Lions, Some methods in the mathematical analysis of systems and their control Science Press, Beijing, Gordon and Breach, New York (1981)
[21] G. Milton, The theory of composites, Cambridge University Press (2001) [22] F. Murat, Compacit´e par compensation, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 5, pp.489-507 (1978)
[23] F. Murat, L. Tartar, H-convergence S´eminaire d’Analyse Fonctionnelle et Num´erique de l’Universit´e d’Alger (1977). English translation in ”Topics in the mathematical modeling of composite materials”, A. Cherkaev and R.V. Kohn ed., series ”Progress in Nonlinear Differential Equations and their Applications”, 31, Birkh¨auser, Boston (1997)
[24] G. Nguetseng, A general convergence result for a functional related to the theory of homogenization SIAM J. Math. Anal. 20 (1989) 608-629
[25] O. Oleinik, A. Shamaev, G. Yosifian, Mathematical Problems in Elasticity and Homogenization Studies in Mathematics an Its Application 26 Elsevier, Amsterdam (1992)
[26] G. Papanicolaou, S. Varadhan, Boundary value problems with rapidly oscillating random coefficients Colloquia Mathematica Societatis J´anos Bolyai, North-Holland, Amsterdam (1982) 835-873
[27] E. Sanchez-Palencia, Non-Homogeneous Media and Vibration Theory Springer Lecture Notes in Physics 129 (1980)
[28] S. Spagnolo, Sulla convergenza delle soluzioni di equazioni paraboliche ed ellittiche Ann. Sc. Norm. Sup. Pisa Cl. Sci. (3) 22 (1968) 571-597
[29] S. Spagnolo, Convergence in energy for elliptic operators Proc. Third Symp. Numer. Solut. Partial Diff. Equat. (College Park 1975), B. Hubbard ed., Academic Press, San Diego (1976) 469-498
[30] L. Tartar, Quelques remarques sur l’homog´en´eisation Proc. of the Japan-France Seminar 1976 ”Functional Analysis and Numerical Analysis”, Japan Society for the Promotion of Sciences (1978) 469-482
[31] L. Tartar, Compensated compactness and partial differential equations, in Nonlinear Analysis and Mechanics: Heriot-Watt Symposium vol. IV, pp.136-212, Pitman (1979)
[32] L. Tartar, The General Theory Of Homogenization, Lecture notes of the Unione Matematica Italiana, 7, Springer (2010)
[33] V. Zhikov, S. Kozlov, O. Oleinik, Homogenization of Differential Operators Springer, Berlin, (1995)
There are many books concerning different aspects of homogenization theory. Choose what interests you. Hope this helps