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Infinite dimensional exponential attractors for a non–autonomous reaction–diffusion system
Author(s) -
Efendiev Messoud,
Miranville Alain,
Zelik Sergey
Publication year - 2003
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310004
Subject(s) - attractor , mathematics , exponential function , exponential growth , fractal , curse of dimensionality , reaction–diffusion system , entropy (arrow of time) , pure mathematics , mathematical analysis , physics , statistics , quantum mechanics
In this article, we give a construction of exponential attractors that is valid for general translation–compact non–autonomous systems. Since they are generally infinite dimensional, we replace, compared with the standard definition, the condition of finite fractal dimensionality of exponential attractors by requiring that their epsilon–entropy have the same form as that of the uniform attractor. As an example, we prove the existence of an (infinite dimensional) exponential attractor for a reaction–diffusion system.