Investigations of retarded PDEs of second order in time using the method of inertial manifolds with delay

Alexander V. Rezounenko[1]

  • [1] Kharkov University, Department of Mechanics and Mathematics, 4 Svobody sqr., Kharkov 61077 (Ukraine)

Annales de l’institut Fourier (2004)

  • Volume: 54, Issue: 5, page 1547-1564
  • ISSN: 0373-0956

Abstract

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Inertial manifold with delay (IMD) for dissipative systems of second order in time is constructed. This result is applied to the study of different asymptotic properties of solutions. Using IMD, we construct approximate inertial manifolds containing all the stationary solutions and give a new characterization of the K-invariant manifold.

How to cite

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Rezounenko, Alexander V.. "Investigations of retarded PDEs of second order in time using the method of inertial manifolds with delay." Annales de l’institut Fourier 54.5 (2004): 1547-1564. <http://eudml.org/doc/116151>.

@article{Rezounenko2004,
abstract = {Inertial manifold with delay (IMD) for dissipative systems of second order in time is constructed. This result is applied to the study of different asymptotic properties of solutions. Using IMD, we construct approximate inertial manifolds containing all the stationary solutions and give a new characterization of the K-invariant manifold.},
affiliation = {Kharkov University, Department of Mechanics and Mathematics, 4 Svobody sqr., Kharkov 61077 (Ukraine)},
author = {Rezounenko, Alexander V.},
journal = {Annales de l’institut Fourier},
keywords = {approximate inertial manifolds; inertial manifolds with delay; retarded non-linear partial differential equations; retarded nonlinear partial differential equations},
language = {eng},
number = {5},
pages = {1547-1564},
publisher = {Association des Annales de l'Institut Fourier},
title = {Investigations of retarded PDEs of second order in time using the method of inertial manifolds with delay},
url = {http://eudml.org/doc/116151},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Rezounenko, Alexander V.
TI - Investigations of retarded PDEs of second order in time using the method of inertial manifolds with delay
JO - Annales de l’institut Fourier
PY - 2004
PB - Association des Annales de l'Institut Fourier
VL - 54
IS - 5
SP - 1547
EP - 1564
AB - Inertial manifold with delay (IMD) for dissipative systems of second order in time is constructed. This result is applied to the study of different asymptotic properties of solutions. Using IMD, we construct approximate inertial manifolds containing all the stationary solutions and give a new characterization of the K-invariant manifold.
LA - eng
KW - approximate inertial manifolds; inertial manifolds with delay; retarded non-linear partial differential equations; retarded nonlinear partial differential equations
UR - http://eudml.org/doc/116151
ER -

References

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