A class of infinite-dimensional dissipative dynamical systems is defined for which there exists a unique equilibrium point, and the rate of convergence to this point of the trajectories of a dynamical system from the above class is exponential. All the trajectories of the system converge to this point as t → +∞, no matter what the initial conditions are. This class consists of strongly dissipative systems. An example of such systems is provided by passive systems in network theory (see, e.g., MR0601947 (83m:45002)).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba57-1-3,
author = {A. G. Ramm},
title = {Attractors of Strongly Dissipative Systems},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {57},
year = {2009},
pages = {25-31},
zbl = {1175.37079},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba57-1-3}
}
A. G. Ramm. Attractors of Strongly Dissipative Systems. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 57 (2009) pp. 25-31. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba57-1-3/