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Russian Mathematical Surveys, 2002, Volume 57, Issue 4, Pages 753–784
DOI: https://doi.org/10.1070/RM2002v057n04ABEH000550 (Mi rm550) 		 
This article is cited in 22 scientific papers (total in 22 papers)

Infinite-dimensional trajectory attractors of elliptic boundary-value problems in cylindrical domains

A. Mielkea, S. V. Zelikb

a University of Stuttgart, Mathematical Institute A
b Institute for Information Transmission Problems, Russian Academy of Sciences
English version PDF (383 kB) Citations (22) Russian version article
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DOI: https://doi.org/10.1070/RM2002v057n04ABEH000550
Abstract: This paper is a study of an abstract model of a second-order non-linear elliptic boundary-value problem in a cylindrical domain by the methods of the theory of dynamical systems. It is shown that, under some natural conditions, the essential solutions of the problem in question are described by means of the global attractor of the corresponding trajectory dynamical system, and this attractor can have infinite fractal dimension and infinite topological entropy. Moreover, sharp upper and lower bounds are obtained for the Kolmogorov $\varepsilon$-entropy of these attractors.
Received: 05.04.2002
Bibliographic databases:
Document Type: Article
MSC: Primary 35J25, 35J65; Secondary 35B41, 37A35, 37B40, 37C45, 35K57
Language: English
Original paper language: Russian
Citation: A. Mielke, S. V. Zelik, “Infinite-dimensional trajectory attractors of elliptic boundary-value problems in cylindrical domains”, Russian Math. Surveys, 57:4 (2002), 753–784
Citation in format AMSBIB
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\by A.~Mielke, S.~V.~Zelik
\paper Infinite-dimensional trajectory attractors of elliptic boundary-value problems in cylindrical domains
\jour Russian Math. Surveys
\yr 2002
\vol 57
\issue 4
\pages 753--784
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    • This publication is cited in the following 22 articles:
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