Homogenization of attractors for semilinear parabolic equations on manifolds with complicated microstructure

Annali di Matematica Pura ed Applicata

Volumn 172, Issue 1, 1997, Pages 297-322

  Boutet De Monvel, L ^a   Chueshov, I D ^a,b   Khruslov, E Y A ^a,c  

^a INSTITUT DE MATHÉMATIQUES DE JUSSIEU   (France)

^b University of Kharkov   (Ukraine)

^c B VERKIN INSTITUTE FOR LOW TEMPERATURE PHYSICS AND ENGINEERING   (Ukraine)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0003389323     PISSN: 03733114     EISSN: 16181891     Source Type: Journal    
DOI: 10.1007/BF01782617     Document Type: Article

References (17)

1. A. V. BABIN - M. J. VISHIK, Attractors of Evolution Equations, Amsterdam, North-Holland (1992).
2. L. BOUTET DE MONVEL - E. YA. KHRUSLOV, Homogenization on Riemannian manifolds, BiBoS Preprint 560/93, Bielefeld (1993) (to appear in the Proceedings «Composite Media», Trieste, 1994).
3. I. D. CHUESHOV, A problem on non-linear oscillations of shallow shell in a quasistatic formulation, Math. Notes, 47 (1990), pp. 401-407.
4. I. D. CHUESHOV, Global attractors for non-linear problems of mathematical physics, Russian Math. Surveys, 43, 3 (1993), pp. 133-161.
5. I. D. CHUESHOV, Quasistatic version of the system of von Karman equations, Matem. Physika, Analiz, Geometriya, 1, 1 (1994), pp. 149-167 (Russian).
6. J.-M. GHIDAGLIA - M. MARION - R. TEMAM, Generalization of the Sobolev-Lieb-Thirring inequalities and applications of attractors, Diff. Integ. Eq., 1 (1988), pp. 67-92.
7. J. K. HALE, Asymptotic Behavior of Dissipative Systems, Amer. Math. Soc. Providence, (1988).
8. J. K. HALE - G. RAUGEL, Reaction-diffusion equations on thin domains, J. Math. Pures Appl., 71 (1992), pp. 33-95.
9. D. HENRY, Geometric Theory of Semilinear Parabolic Equations, Springer, New York (1981).
10. L. V. KAPITANSKY - I. N. KOSTIN, Attractors of non-linear evolution equations and their approximations, Leningrad Math. J., 2 (1991), pp. 97-117.
11. E. YA. KHRUSLOV, Homogenized diffusion model in cracked-porous media, Dokl. Akad. Nauk SSSR, 309 (1989), pp. 332-335 (Russian).
12. E. YA. KHRUSLOV, Homogenized model of strongly inhomogeneous medium with memory, Uspeckhi Math. Nauk, 45, 1 (1990), pp. 197-199 (Russian).
13. E. YA. KHRUSLOV, Homogenized models of composite media, in Composite Media and Homogenized Theory (Eds. G. DAL MASO, G. F. DELL'ANTONIO) Birkhauser (1991), pp. 159-182.
14. E. YA. KHRUSLOV, Homogenized models of strongly inhomogeneous media, talk on Math. Congress Zurich (1994) (to be published).
15. O. A. LADYZENSKAYA - V. A. SOLONNIKOV - N. N. URALTSEVA, Linear and quasilinear equations of parabolic type, Amer. Math. Soc., Providence (1968).
16. J. MORITA - S. JIMBO, Ordinary differential equations on inertial manifolds for reaction-diffusion systems in a singularity perturbed domain with several thin channels, J. Dyn. Diff. Eqs., 4 (1992), pp. 65-93.
17. R. TEMAM, Infinite dimensional systems, in Mechanics and Physics, Springer, New York (1988).