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

This article is cited in 16 scientific papers (total in 16 papers)

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

Full text: PDF file (265 kB)
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English version:
Mathematical Notes, 1999, 65:6, 790–792

Bibliographic databases:

Received: 15.02.1999

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
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\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
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\crossref{https://doi.org/10.4213/mzm1132}
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\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}
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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  mathnet  crossref  crossref  mathscinet  zmath  isi
    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  crossref  mathscinet  zmath  isi
    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  crossref  mathscinet  zmath  isi  scopus
    4. Zelik, SV, “The attractor for a nonlinear hyperbolic equation in the unbounded domain”, Discrete and Continuous Dynamical Systems, 7:3 (2001), 593  crossref  mathscinet  zmath  isi  scopus  scopus
    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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    6. Lord, GJ, “Topological and epsilon-entropy for large volume limits of discretized parabolic equations”, SIAM Journal on Numerical Analysis, 40:4 (2002), 1311  crossref  mathscinet  zmath  isi  scopus  scopus
    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  crossref  mathscinet  zmath  isi  scopus
    8. Efendiev, M, “Infinite dimensional exponential attractors for a non-autonomous react ion-diffusion system”, Mathematische Nachrichten, 248 (2003), 72  crossref  mathscinet  zmath  isi  scopus
    9. Lord, GJ, “Numerical computation of epsilon-entropy for parabolic equations with analytic solutions”, Physica D-Nonlinear Phenomena, 194:1–2 (2004), 65  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    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  crossref  mathscinet  zmath  isi
    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  crossref  mathscinet  zmath  adsnasa  isi  scopus
    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  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    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  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    14. Scheel, A, “Lattice differential equations embedded into reaction-diffusion systems”, Proceedings of the Royal Society of Edinburgh Section A-Mathematics, 139 (2009), 193  crossref  mathscinet  zmath  isi  scopus  scopus
    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  crossref  mathscinet  zmath  isi  scopus  scopus
    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  crossref  mathscinet  zmath  isi  scopus  scopus
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