The C 1 stability of slow manifolds for a system of singularly perturbed evolution equations

Daniel Ševčovič

Commentationes Mathematicae Universitatis Carolinae (1995)

  • Volume: 36, Issue: 1, page 89-107
  • ISSN: 0010-2628

Abstract

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In this paper we investigate the singular limiting behavior of slow invariant manifolds for a system of singularly perturbed evolution equations in Banach spaces. The aim is to prove the C 1 stability of invariant manifolds with respect to small values of the singular parameter.

How to cite

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Ševčovič, Daniel. "The C$^1$ stability of slow manifolds for a system of singularly perturbed evolution equations." Commentationes Mathematicae Universitatis Carolinae 36.1 (1995): 89-107. <http://eudml.org/doc/247704>.

@article{Ševčovič1995,
abstract = {In this paper we investigate the singular limiting behavior of slow invariant manifolds for a system of singularly perturbed evolution equations in Banach spaces. The aim is to prove the C$^\{1\}$ stability of invariant manifolds with respect to small values of the singular parameter.},
author = {Ševčovič, Daniel},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {singularly perturbed evolution equations; C$^1$ stability of inertial manifolds; stability of inertial manifolds; slow invariant manifolds; evolution equations in Banach spaces},
language = {eng},
number = {1},
pages = {89-107},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {The C$^1$ stability of slow manifolds for a system of singularly perturbed evolution equations},
url = {http://eudml.org/doc/247704},
volume = {36},
year = {1995},
}

TY - JOUR
AU - Ševčovič, Daniel
TI - The C$^1$ stability of slow manifolds for a system of singularly perturbed evolution equations
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1995
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 36
IS - 1
SP - 89
EP - 107
AB - In this paper we investigate the singular limiting behavior of slow invariant manifolds for a system of singularly perturbed evolution equations in Banach spaces. The aim is to prove the C$^{1}$ stability of invariant manifolds with respect to small values of the singular parameter.
LA - eng
KW - singularly perturbed evolution equations; C$^1$ stability of inertial manifolds; stability of inertial manifolds; slow invariant manifolds; evolution equations in Banach spaces
UR - http://eudml.org/doc/247704
ER -

References

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  9. Ševčovič D., Limiting behavior of global attractors for singularly perturbed beam equations with strong damping, Comment. Math. Univ. Carolinae 32 (1991), 45-60. (1991) MR1118289
  10. Sviridyuk G.A., The Deborah number and a class of semilinear equations of Sobolev type (English translation), Soviet. Math. Doklady 44 No.1 (1992), 297-301. (1992) MR1152892
  11. Sviridyuk G.A., Sukacheva T.G., Cauchy problem for a class of semilinear equations of Sobolev type (English translation), Sibirskii Matem. Zhurnal 31 No.5 (1990), 120-127. (1990) MR1088921
  12. Vanderbauwhede A., Van Gils V.A., Center manifolds and contraction on a scale of Banach spaces, J. of Funct. Analysis 72 (1987), 209-224. (1987) MR0886811

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