A modified strong squeezing property and the existence of inertial manifolds of semiflows

Norbert Koksch

Archivum Mathematicum (2000)

  • Volume: 036, Issue: 5, page 477-486
  • ISSN: 0044-8753

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Koksch, Norbert. "A modified strong squeezing property and the existence of inertial manifolds of semiflows." Archivum Mathematicum 036.5 (2000): 477-486. <http://eudml.org/doc/248567>.

@article{Koksch2000,
author = {Koksch, Norbert},
journal = {Archivum Mathematicum},
keywords = {semiflow; inertial manifold; asymptotic phase; cone invariance property},
language = {eng},
number = {5},
pages = {477-486},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {A modified strong squeezing property and the existence of inertial manifolds of semiflows},
url = {http://eudml.org/doc/248567},
volume = {036},
year = {2000},
}

TY - JOUR
AU - Koksch, Norbert
TI - A modified strong squeezing property and the existence of inertial manifolds of semiflows
JO - Archivum Mathematicum
PY - 2000
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 036
IS - 5
SP - 477
EP - 486
LA - eng
KW - semiflow; inertial manifold; asymptotic phase; cone invariance property
UR - http://eudml.org/doc/248567
ER -

References

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  1. 1. P. Constantin C. Foias B. Nicolaenko, and R. Temam, Nouveaux resultats sur les variétés inertielles pour les équations différentielles dissipatives, (New results on the inertial manifolds for dissipative differential equations), C. R. Acad. Sci., Paris, Ser. I 302 (1986), 375–378. (1986) MR0838393
  2. 2. P. Constantin C. Foias B. Nicolaenko, and R. Temam, Integral manifolds and inertial manifolds for dissipative partial differential equations, Applied Mathematical Sciences, vol. 70, Springer, 1989. (1989) MR0966192
  3. 3. C. Foias B. Nicolaenko G.R. Sell, and R. Temam, Variétés inertielles pour l’équation de Kuramoto-Sivashinsky, (Inertial manifolds for the Kuramoto-Sivashinsky equation), C. R. Acad. Sci., Paris, Ser. I 301 (1985), 285–288. (1985) MR0803219
  4. 4. C. Foias G.R. Sell, and R. Temam, Variétés inertielles des équations différentielles dissipatives, (Inertial manifolds for dissipative differential equations), C. R. Acad. Sci., Paris, Ser. I 301 (1985), 139–141. (1985) MR0801946
  5. 5. C. Foias G.R. Sell, and R. Temam, Inertial manifolds for nonlinear evolutionary equations, J. of Differential Equations 73 (1988), 309–353. (1988) MR0943945
  6. 6. C. Foias G.R. Sell, and E.S. Titi, Exponential tracking and approximation of inertial manifolds for dissipative nonlinear equations, J. of Dynamics and Differential Equations 1 (1989), no. 2, 199–244. (1989) MR1010966
  7. 7. D. Henry, Geometric theory of semilinear parabolic equations, Lecture Notes in Mathematics, vol. 850, Springer, 1981. (1981) Zbl0456.35001MR0610244
  8. 8. N. Koksch, A comparison principle approach to the existence and smootheness of integral manifolds, Habilitation, Fak. Mathematik und Naturwissenschaften der TU Dresden, 1999. (1999) 
  9. 9. M. Miklavčič, Applied functional analysis and partial differential equations, World Scientific, Singnapur, New Jersey, London, Hong Kong, 1998. (1998) MR1784426
  10. 10. H. Ninomiya, Some remarks on inertial manifolds, J. Math. Kyoto Univ. 32 (1992), no. 4, 667–688. (1992) Zbl0815.35037MR1194108
  11. 11. J.C. Robinson, Inertial manifolds and the cone condition, Dyn. Syst. Appl. 2 (1993), no. 3, 311–330. (1993) Zbl0787.34036MR1233854
  12. 12. J.C. Robinson, The asymptotic completeness of inertial manifolds, Nonlinearity 9 (1996), 1325–1340. (1996) Zbl0898.35016MR1416479
  13. 13. A.V. Romanov, Sharp estimates of the dimension of inertial manifolds for nonlinear parabolic equations, Russ. Acad. Sci., Izv., Math. 43 (1994), no. 1, 31–47. (1994) MR1243350
  14. 14. R. Temam, Infinite-dimensional dynamical systems in mechanics and physics, 2nd ed., Applied Mathematical Sciences, vol. 68, Springer, New York, 1997. (1997) MR1441312

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