Attractors of the reaction-diffusion systems with rapidly oscillating coefficients and their homogenization
Annales de l'I.H.P. Analyse non linéaire, Tome 19 (2002) no. 6, pp. 961-989. 
@article{AIHPC_2002__19_6_961_0,
     author = {Efendiev, M. and Zelik, S.},
     title = {Attractors of the reaction-diffusion systems with rapidly oscillating coefficients and their homogenization},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {961--989},
     publisher = {Elsevier},
     volume = {19},
     number = {6},
     year = {2002},
     mrnumber = {1939092},
     zbl = {1036.35038},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2002__19_6_961_0/}
}
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Efendiev, M.; Zelik, S. Attractors of the reaction-diffusion systems with rapidly oscillating coefficients and their homogenization. Annales de l'I.H.P. Analyse non linéaire, Tome 19 (2002) no. 6, pp. 961-989. http://www.numdam.org/item/AIHPC_2002__19_6_961_0/

[1] Babin A.V., Vishik M.I., Attractors of Evolutionary Equations, North-Holland, Amsterdam, 1992. | MR | Zbl

[2] Bensoussan A., Lions J.-L., Papanicolaou G., Asymptotic Analysis for Periodic Structures, North-Holland, Amsterdam, 1978. | MR | Zbl

[3] Bourgeat A., Pankratov L., Homogenization of semilinear parabolic equations in domains with spherical traps, Appl. Anal. 64 (3-4) (1997) 303-317. | MR | Zbl

[4] Freitas P., Rocha C., Lyapunov functional and stability for FitzHugh-Nagumo systems, JDE 169 (2001) 208-227. | MR | Zbl

[5] De Giorgi E., Spagnolo S., Sulla convergenza degli integrali dell'energia per operatori ellittici del secondo ordine, Boll. Unione Mat. Ital 8 (1973) 391-411. | MR | Zbl

[6] Hale J., Asymptotic Behaviour of Dissipative Systems, Math. Surveys Monographs, 25, American Mathematical Society, Providence, RI, 1987. | MR | Zbl

[7] Kozlov S., Averaging differential equations with almost-periodic rapidly oscillating coefficients, Math. USSR Sb. 35 (4) (1979) 481-498. | Zbl

[8] Kuznetsov Y., Elements of Applied Bifurkation Theory, Applied Math. Sciences, 112, Springer-Verlag, New York, 1995. | MR | Zbl

[9] Ladyzhenskaya O., Solonnikov V., Uraltseva N., Linear and Quasilinear Parabolic Equations, Nauka, Moscow, 1967.

[10] Levitan B., Almost-periodic Functions, Gostekhizdat, Moscow, 1953. | MR | Zbl

[11] Levitan B., Zhikov V., Almost-periodic Functions and Differential Equations, Moscow Univ. Press, Moscow, 1978. | MR | Zbl

[12] Pankratov L., Chueshov I., Homogenization of attractors of non-linear hyperbolic equations with asymptotically degenerate coefficients, Sb. Math. 190 (9) (1999) 1325-1352. | MR | Zbl

[13] Temam R., Infinite Dimensional Dynamical Systems in Mechanics and Physics, Springer-Verlag, New York, 1988. | MR | Zbl

[14] Triebel H., Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam, 1978. | MR | Zbl

[15] Vishik M., Asymptotic Behaviour of Solutions of Evolutionary Equations, Cambridge Univ. Press, Cambridge, 1992. | MR | Zbl

[16] M. Vishik, Attractors of Equations Arising in Mathematical Physics with Rapidly Oscillating Terms and their Averadging, Talk on the Conference Dedicated to the 60th Birthday of R. Temam (Paris, Poitiers, 2000) (joint work with B. Fiedler).

[17] Vishik M., Zelik S., The regular attractor for a non-linear elliptic system in a cylindrical domain, Math. Sb. 190 (6) (1999) 803-834. | MR | Zbl

[18] Zelik S., The attractor for a nonlinear reaction-diffusion system with a supercritical nonlinearity and it's dimension, Rend. Acad. Naz. Sci. XL Mem. Mat. Appl. 24 (2000) 1-25. | MR

[19] Zelik S., The dynamics of fast non-autonomous travelling waves and homogenization, in: Carrive M., (Eds.), Actes des journées « Jeunes numériciens » en l'honneur du 60ème anniversaire du Professeur Roger Temam, Poitiers, France, Mars 9-10, 2000, Poitou-Charentes : Atlantique, 2001, pp. 131-142, (English). | Zbl

[20] Zhikov V., Kozlov S., Oleinik O., Homogenization of differential operators and integral functionals, Springer-Verlag, Berlin, 1994. | MR | Zbl