Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Bücher
Zeitschriften
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
MTZ-Fachkongress

Antriebe und Energiesysteme von morgen


Austausch von Automobil- und Energiewirtschaft

Am 14./15. Mai geht es in Chemnitz um die Mobilitätswende durch Elektro- und Wasserstofffahrzeuge.
Erweiterte Suche
Anmelden
nach oben
Erschienen in:
Preliminaries Kapitel lesen Erstes Kapitel lesen

2018 | OriginalPaper | Buchkapitel

2. Trajectory Dynamical Systems and Their Attractors

verfasst von : Messoud Efendiev

Erschienen in: Symmetrization and Stabilization of Solutions of Nonlinear Elliptic Equations

Verlag: Springer International Publishing

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

We start with the definition of Kolmogorov ε-entropy, via which we define fractal dimension of the compact set in the metric space. We will use these two concepts in the sequel.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren
Vorheriges Kapitel Preliminaries
Nächstes Kapitel Symmetry and Attractors: The Case N ≤ 3
Fußnoten
1
Actually we use here the letter ω in two different senses: for the ω-limit set and for a bounded polyhedral domain in \(\mathbb {R}^n\); \(\Omega _+:=\mathbb {R}\times \omega \), \(\Omega =\mathbb {R}\times \omega \). We hope that it will not lead to a misunderstanding for the readers.
 
Literatur
1.
A. V. Babin and M. I. Vishik. Attractors of evolution equations. Transl. from the Russian by A. V. Babin. English. Amsterdam etc.: North-Holland, 1992, pp. x + 532.
8.
A. V. Babin. “Attractor of the generalized semigroup generated by an elliptic equation in a cylindrical domain”. In: Russian Acad. Sci. Izv. Math. 44 (1995), pp. 207–223.MathSciNetCrossRef
13.
H. Berestycki, L. Caffarelli, and L. Nirenberg. “Monotonicity for elliptic equations in unbounded Lipschitz domains.” English. In: Commun. Pure Appl. Math. 50.11 (1997), pp. 1089–1111.MathSciNetCrossRef
15.
H. Berestycki, M. A. Efendiev, and S. Zelik. “Dynamical approach for positive solutions of semilinear elliptic problems in unbounded domains.” English. In: Nonlinear Bound. Value Probl. 14 (2004), pp. 3–15.
18.
H. Berestycki and L. Nirenberg. “On the method of moving planes and the sliding method.” English. In: Bol. Soc. Bras. Mat., Nova Sér. 22.1 (1991), pp. 1–37.
19.
H. Berestycki and L. Nirenberg. Some qualitative properties of solutions of semilinear elliptic equations in cylindrical domains. English. Analysis, et cetera, Res. Pap. in Honor of J. Moser’s 60th Birthd., 115–164 (1990). 1990.CrossRef
21.
H. Berestycki, L. Caffarelli, and L. Nirenberg. “Further qualitative properties for elliptic equations in unbounded domains.” English. In: Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 25.1-2 (1997), pp. 69–94.
23.
H. Berestycki and P.-L. Lions. “Nonlinear scalar field equations. I: Existence of a ground state.” English. In: Arch. Ration. Mech. Anal. 82 (1983), pp. 313–345.
25.
H. Berestycki and L. Nirenberg. “Travelling fronts in cylinders.” English. In: Ann. Inst. Henri Poincaé, Anal. Non Linéaire 9.5 (1992), pp. 497–572.MathSciNetCrossRef
29.
P. Brunovský, X. Mora, P. Poláčik, and J. Solà-Morales. “Asymptotic behavior of solutions of semilinear elliptic equations on an unbounded strip.” English. In: Acta Math. Univ. Comen., New Ser. 60.2 (1991), pp. 163–183.
30.
J. Busca and P. Felmer. “Qualitative properties of some bounded positive solutions to scalar field equations.” English. In: Calc. Var. Partial Differ. Equ. 13.2 (2001), pp. 191–211.MathSciNetCrossRef
31.
A. Calsina, X. Mora, and J. Solà-Morales. “The dynamical approach to elliptic problems in cylindrical domains, and a study of their parabolic singular limit.” English. In: J. Differ. Equations 102.2 (1993), pp. 244–304.MathSciNetCrossRef
32.
V. V. Chepyzhov and M. I. Vishik. “Evolution equations and their trajectory attractors.” English. In: J. Math. Pures Appl. (9) 76.10 (1997), pp. 913–964.
33.
V. V. Chepyzhov and M. I. Vishik. “Non-autonomous evolutionary equations with translation-compact symbols and their attractors.” English. In: C. R. Acad. Sci., Paris, Sér. I 321.2 (1995), pp. 153–158.
34.
V. V. Chepyzhov and M. I. Vishik. “Trajectory attractors for evolution equations.” English. In: C. R. Acad. Sci., Paris, Sér. I 321.10 (1995), pp. 1309–1314.
35.
V. Chepyzhov and M. Vishik. Attractors for equations of mathematical physics. English. Providence, RI: American Mathematical Society (AMS), 2002, pp. xi +363.
36.
V. Chepyzhov and M. Vishik. “Attractors of non-autonomous dynamical systems and their dimension.” English. In: J. Math. Pures Appl. (9) 73.3 (1994), pp. 279–333.
40.
M. Dauge. Elliptic boundary value problems on corner domains. Smoothness and asymptotics of solutions. English. Berlin etc.: Springer-Verlag, 1988, pp. viii + 259.
46.
M. A. Efendiev. Attractors for degenerate parabolic type equations. English. Providence, RI: American Mathematical Society (AMS); Madrid: Real Sociedad Matemática Española (RSME), 2013, pp. x + 221.MATH
47.
M. A. Efendiev. Evolution equations arising in the modelling of life sciences. English. New York, NY: Birkhäuser/Springer, 2013, pp. xii + 217.CrossRef
48.
M. A. Efendiev. Finite and infinite dimensional attractors for evolution equations of mathematical physics. English. Tokyo: Gakkōtosho, 2010, pp. ii + 239.
49.
M. A. Efendiev. Fredholm structures, topological invariant and applications. English. Springfield, MO: American Institute of Mathematical Sciences, 2009, pp. x + 205.
52.
M. A. Efendiev and S. V. Zelik. “The attractor for a nonlinear reaction-diffusion system in an unbounded domain.” English. In: Commun. Pure Appl. Math. 54.6 (2001), pp. 625–688.MathSciNetCrossRef
65.
B. Gidas, W.-M. Ni, and L. Nirenberg. “Symmetry and related properties via the maximum principle.” English. In: Commun. Math. Phys. 68 (1979), pp. 209–243.MathSciNetCrossRef
67.
J. K. Hale. Asymptotic behavior of dissipative systems. English. Providence, RI: American Mathematical Society, 1988, pp. ix + 198.
69.
V. Hutson, J. S. Pym, and M. J. Cloud. Applications of functional analysis and operator theory. 2nd ed. English. 2nd ed. Amsterdam: Elsevier, 2005, pp. xiv + 426.
73.
A. Kolmogorov and V. Tikhomirov. “ε-entropy and ε-capacity of sets in function spaces.” English. In: Transl., Ser. 2, Am. Math. Soc. 17 (1959), pp. 227–364.
74.
M. Krasnosel’skij. Topological methods in the theory of nonlinear integral equations. Translated by A.H. Armstrong. English. International Series of Monographs on Pure and Applied Mathematics. 45. Oxford etc.: Pergamon Press. XI, 395 p. (1964). 1964.
75.
M. K. Kwong. “Uniqueness of positive solutions of Δu − u + up = 0 in Rn.” English. In: Arch. Ration. Mech. Anal. 105.3 (1989), pp. 243–266.
76.
O. Ladyzhenskaya and N. Ural’tseva. Linear and quasilinear elliptic equations. Mathematics in Science and Engineering. Elsevier Science, 1968.MATH
78.
J. Lions and E. Magenes. Problèmes aux limites non homogenes et applications. Vol. 1, 2. French. Paris: Dunod 1: XIX, 372 p.; 2: XV, 251 p. (1968). 1968.
86.
H. H. Schaefer. Topological vector spaces. 4th corr. printing. English. Graduate Texts in Mathematics, 3. New York-Heidelberg-Berlin: Springer- Verlag. XI, 294 p. DM 48.00; $ 28.40 (1980). 1980.
98.
R. Temam. Infinite-dimensional dynamical systems in mechanics and physics. 2nd ed. English. 2nd ed. New York, NY: Springer, 1997, pp. xxi + 648.CrossRef
101.
H. Triebel. Interpolation theory, function spaces, differential operators. 2nd rev. a. enl. ed. English. 2nd rev. a. enl. ed. Leipzig: Barth, 1995, p. 532.
103.
M. Vishik and S. Zelik. “The trajectory attractor of a nonlinear elliptic system in a cylindrical domain.” English. In: Sb. Math. 187.12 (1996), 1755–1789 (1996); translation from mat. sb. 187, no. 12, 21–56.MathSciNetCrossRef
104.
A. Vol’pert and S. Khudyaev. Analysis in classes of discontinuous functions and equations of mathematical physics. English. Mechanics: Analysis, 8. Dordrecht - Boston - Lancaster: Martinus Nijhoff Publishers, a member of the Kluwer Academic Publishers Group. XVIII, 678 p. Dfl. 340.00; $ 117.50; £86.50 (1985). 1985.
106.
E. Zeidler. Nonlinear functional analysis and its applications. Volume I: Fixed-point theorems. Translated from the German by Peter R. Wadsack. 2. corr. printing. English. 2. corr. printing. New York: Springer-Verlag, 1993, pp. xxiii + 909.
107.
S. Zelik. “The dynamics of fast non-autonomous travelling waves and homogenization.” English. In: Actes des journées “Jeunes numériciens” en l’honneur du 60ème anniversaire du Professeur Roger Temam, Poitiers, France, Mars 9–10, 2000. Poitou-Charentes: Atlantique, 2001, pp. 131–142.
108.
S. Zelik. “A trajectory attractor of a nonlinear elliptic system in an unbounded domain.” English. In: Math. Notes 63.1 (1998), 120–123 (1998); translation from mat. zametki 63, no. 1, 135–138.MathSciNetCrossRef
Metadaten
Titel
Trajectory Dynamical Systems and Their Attractors
verfasst von
Messoud Efendiev
Copyright-Jahr
2018
Buch
Symmetrization and Stabilization of Solutions of Nonlinear Elliptic Equations

Print ISBN: 978-3-319-98406-3

Electronic ISBN: 978-3-319-98407-0

Copyright-Jahr: 2018

DOI
https://doi.org/10.1007/978-3-319-98407-0_2

Premium Partner

    Bildnachweise