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 Mat. Zametki, 1999, Volume 65, Issue 6, Pages 941–944 (Mi mz1132)

Brief Communications

An attractor of a nonlinear system of reaction-diffusion equations in $\mathbb R^n$ and estimates for its $\epsilon$-entropy

S. V. Zelik

Institute for Information Transmission Problems, Russian Academy of Sciences

DOI: https://doi.org/10.4213/mzm1132

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English version:
Mathematical Notes, 1999, 65:6, 790–792

Bibliographic databases:

Citation: S. V. Zelik, “An attractor of a nonlinear system of reaction-diffusion equations in $\mathbb R^n$ and estimates for its $\epsilon$-entropy”, Mat. Zametki, 65:6 (1999), 941–944; Math. Notes, 65:6 (1999), 790–792

Citation in format AMSBIB
\Bibitem{Zel99} \by S.~V.~Zelik \paper An attractor of a~nonlinear system of reaction-diffusion equations in~$\mathbb R^n$ and estimates for its $\epsilon$-entropy \jour Mat. Zametki \yr 1999 \vol 65 \issue 6 \pages 941--944 \mathnet{http://mi.mathnet.ru/mz1132} \crossref{https://doi.org/10.4213/mzm1132} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1728296} \zmath{https://zbmath.org/?q=an:0948.35016} \transl \jour Math. Notes \yr 1999 \vol 65 \issue 6 \pages 790--792 \crossref{https://doi.org/10.1007/BF02675597} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000083786600038} 

• http://mi.mathnet.ru/eng/mz1132
• https://doi.org/10.4213/mzm1132
• http://mi.mathnet.ru/eng/mz/v65/i6/p941

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. S. V. Zelik, “The attractor of a quasilinear hyperbolic equation with dissipation in $\mathbb R^n$: Dimension and $\varepsilon$-entropy”, Math. Notes, 67:2 (2000), 248–251
2. Zelik, SV, “The attractor for a nonlinear reaction-diffusion system in the unbounded domain and Kolmogorov's epsilon-entropy”, Mathematische Nachrichten, 232 (2001), 129
3. Efendiev, MS, “The attractor for a nonlinear reaction-diffusion system in an unbounded domain”, Communications on Pure and Applied Mathematics, 54:6 (2001), 625
4. Zelik, SV, “The attractor for a nonlinear hyperbolic equation in the unbounded domain”, Discrete and Continuous Dynamical Systems, 7:3 (2001), 593
5. 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
6. Lord, GJ, “Topological and epsilon-entropy for large volume limits of discretized parabolic equations”, SIAM Journal on Numerical Analysis, 40:4 (2002), 1311
7. Zelik, SV, “Attractors of reaction-diffusion systems in unbounded domains and their spatial complexity”, Communications on Pure and Applied Mathematics, 56:5 (2003), 584
8. Efendiev, M, “Infinite dimensional exponential attractors for a non-autonomous react ion-diffusion system”, Mathematische Nachrichten, 248 (2003), 72
9. Lord, GJ, “Numerical computation of epsilon-entropy for parabolic equations with analytic solutions”, Physica D-Nonlinear Phenomena, 194:1–2 (2004), 65
10. Efendiev, M, “Global and exponential attractors for nonlinear react ion-diffusion systems in unbounded domains”, Proceedings of the Royal Society of Edinburgh Section A-Mathematics, 134 (2004), 271
11. Efendiev, M, “Infinite-dimensional exponential attractors for nonlinear reaction-diffusion systems in unbounded domains and their approximation”, Proceedings of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences, 460:2044 (2004), 1107
12. Mielke, A, “Infinite-dimensional hyperbolic sets and spatio-temporal chaos in reaction diffusion systems in R-n”, Journal of Dynamics and Differential Equations, 19:2 (2007), 333
13. Zelik, SV, “Spatial and dynamical chaos generated by reaction-diffusion systems in unbounded domains”, Journal of Dynamics and Differential Equations, 19:1 (2007), 1
14. Scheel, A, “Lattice differential equations embedded into reaction-diffusion systems”, Proceedings of the Royal Society of Edinburgh Section A-Mathematics, 139 (2009), 193
15. Goubet O., Maaroufi N., “Entropy by Unit Length for the Ginzburg-Landau Equation on the Line. a Hilbert Space Framework”, Commun. Pure Appl. Anal, 11:3 (2012), 1253–1267
16. Maaroufi N., “Topological Entropy by Unit Length for the Ginzburg-Landau Equation on the Line”, Discret. Contin. Dyn. Syst., 34:2 (2014), 647–662
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