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.
@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}, pages = {1547--1564}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {54}, number = {5}, year = {2004}, doi = {10.5802/aif.2058}, mrnumber = {2127857}, zbl = {1080.35168}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.2058/} }
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 SP - 1547 EP - 1564 VL - 54 IS - 5 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2058/ DO - 10.5802/aif.2058 LA - en ID - AIF_2004__54_5_1547_0 ER -
%0 Journal Article %A Rezounenko, Alexander V. %T Investigations of retarded PDEs of second order in time using the method of inertial manifolds with delay %J Annales de l'Institut Fourier %D 2004 %P 1547-1564 %V 54 %N 5 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2058/ %R 10.5802/aif.2058 %G en %F 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. http://archive.numdam.org/articles/10.5802/aif.2058/
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