Gradient systems of closed operators

Vittorino Pata

Open Mathematics (2009)

  • Volume: 7, Issue: 3, page 487-492
  • ISSN: 2391-5455

Abstract

top
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.

How to cite

top

Vittorino Pata. "Gradient systems of closed operators." Open Mathematics 7.3 (2009): 487-492. <http://eudml.org/doc/269197>.

@article{VittorinoPata2009,
abstract = {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.},
author = {Vittorino Pata},
journal = {Open Mathematics},
keywords = {Semigroup of closed operators; Lyapunov function; Gradient system; Global attractor; semigroup of closed operators; gradient system; global attractor},
language = {eng},
number = {3},
pages = {487-492},
title = {Gradient systems of closed operators},
url = {http://eudml.org/doc/269197},
volume = {7},
year = {2009},
}

TY - JOUR
AU - Vittorino Pata
TI - Gradient systems of closed operators
JO - Open Mathematics
PY - 2009
VL - 7
IS - 3
SP - 487
EP - 492
AB - 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.
LA - eng
KW - Semigroup of closed operators; Lyapunov function; Gradient system; Global attractor; semigroup of closed operators; gradient system; global attractor
UR - http://eudml.org/doc/269197
ER -

References

top
  1. [1] Babin A.V., Vishik M.I., Attractors of evolution equations, North-Holland, Amsterdam, 1992 Zbl0778.58002
  2. [2] Chepyzhov V.V., Vishik M.I., Attractors for equations of mathematical physics, Amer. Math. Soc., Providence, 2002 Zbl0986.35001
  3. [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 Zbl1101.35016
  4. [4] Hale J.K., Asymptotic behavior of dissipative systems, Amer. Math. Soc., Providence, 1988 Zbl0642.58013
  5. [5] Haraux A., Systèmes dynamiques dissipatifs et applications, Masson, Paris, 1991 Zbl0726.58001
  6. [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 Zbl0687.35072
  7. [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 Zbl1152.47046
  8. [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 Zbl1145.35045
  9. [9] Robinson J.C., Infinite-dimensional dynamical systems, Cambridge University Press, Cambridge, 2001 Zbl1026.37500
  10. [10] Sell G.R., You Y., Dynamics of evolutionary equations, Springer, New York, 2002 Zbl1254.37002
  11. [11] Temam R., Infinite-dimensional dynamical systems in mechanics and physics, Springer, New York, 1997 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.