Investigations of retarded PDEs of second order in time using the method of inertial manifolds with delay
Annales de l'Institut Fourier, Volume 54 (2004) no. 5, p. 1547-1564

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.

Nous construisons une variété inertielle avec retard (IMD) pour les systèmes dissipatifs du second ordre en temps. Ce résultat est appliqué à l’étude des propriétés asymptotiques des solutions. En utilisant cette IMD, nous construisons les variétés inertielles approchées contenant toutes les solutions stationnaires et donnons une nouvelle caractérisation de la variété K-invariante.

DOI : https://doi.org/10.5802/aif.2058
Classification:  35R10,  35L05,  37L65
Keywords: approximate inertial manifolds, inertial manifolds with delay, retarded non-linear partial differential equations
@article{AIF_2004__54_5_1547_0,
     author = {Rezounenko, Alexander V.},
     title = {Investigations of retarded PDEs of second order in time using the method of inertial manifolds with delay},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {54},
     number = {5},
     year = {2004},
     pages = {1547-1564},
     doi = {10.5802/aif.2058},
     zbl = {1080.35168},
     mrnumber = {2127857},
     language = {en},
     url = {aif.centre-mersenne.org/item/AIF_2004__54_5_1547_0}
}
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, Volume 54 (2004) no. 5, pp. 1547-1564. doi : 10.5802/aif.2058. https://aif.centre-mersenne.org/item/AIF_2004__54_5_1547_0/

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