A classical result on the existence of global attractors for gradient systems is extended to the case of a semigroup S(t) lacking strong continuity, but satisfying the weaker property of being a closed map for every fixed t ≥ 0.
@article{bwmeta1.element.doi-10_2478_s11533-009-0034-3,
author = {Vittorino Pata},
title = {Gradient systems of closed operators},
journal = {Open Mathematics},
volume = {7},
year = {2009},
pages = {487-492},
zbl = {1191.47078},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0034-3}
}
Vittorino Pata. Gradient systems of closed operators. Open Mathematics, Tome 7 (2009) pp. 487-492. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0034-3/
[1] Babin A.V., Vishik M.I., Attractors of evolution equations, North-Holland, Amsterdam, 1992 | Zbl 0778.58002
[2] Chepyzhov V.V., Vishik M.I., Attractors for equations of mathematical physics, Amer. Math. Soc., Providence, 2002 | Zbl 0986.35001
[3] Conti M., Pata V., Weakly dissipative semilinear equations of viscoelasticity, Commun. Pure Appl. Anal., 2005, 4, 705–720 http://dx.doi.org/10.3934/cpaa.2005.4.705 | Zbl 1101.35016
[4] Hale J.K., Asymptotic behavior of dissipative systems, Amer. Math. Soc., Providence, 1988 | Zbl 0642.58013
[5] Haraux A., Systèmes dynamiques dissipatifs et applications, Masson, Paris, 1991 | Zbl 0726.58001
[6] Ladyzhenskaya O.A., Finding minimal global attractors for the Navier-Stokes equations and other partial differential equations, Russian Math. Surveys, 1987, 42, 27–73 http://dx.doi.org/10.1070/RM1987v042n06ABEH001503 | Zbl 0687.35072
[7] Pata V., Zelik S., A result on the existence of global attractors for semigroups of closed operators, Commun. Pure Appl. Anal., 2007, 6, 481–486 http://dx.doi.org/10.3934/cpaa.2007.6.481 | Zbl 1152.47046
[8] Pata V., Zelik S., Attractors and their regularity for 2-D wave equation with nonlinear damping, Adv. Math. Sci. Appl., 2007, 17, 225–237 | Zbl 1145.35045
[9] Robinson J.C., Infinite-dimensional dynamical systems, Cambridge University Press, Cambridge, 2001 | Zbl 1026.37500
[10] Sell G.R., You Y., Dynamics of evolutionary equations, Springer, New York, 2002 | Zbl 1254.37002
[11] Temam R., Infinite-dimensional dynamical systems in mechanics and physics, Springer, New York, 1997