Abstract
An approach to a homogenized description of solutions of the Cauchy problem for parabolic equations on Riemannian manifolds with complicated microstructure is presented. This approach covers both linear and non-linear cases and makes it possible to establish a connection between global attractors of the initial problem of the homogenized one.
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On leave from Department of Mechanics and Mathematics, Kharkov University, 4 Svobody sqr., 310077 Kharkov, Ukraine.
On leave from Mathematical Division, Institute for Low Temperature Physics, 47 Lenin ave., 310164 Kharkov, Ukraine.
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Boutet de Monvel, L., Chueshov, I.D. & Khruslov, E.Y. Homogenization of attractors for semilinear parabolic equations on manifolds with complicated microstructure. Annali di Matematica pura ed applicata 172, 297–322 (1997). https://doi.org/10.1007/BF01782617
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DOI: https://doi.org/10.1007/BF01782617