Gradient systems of closed operators

• Autorzy: Vittorino Pata
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Semigroup of closed operators; Lyapunov function; Gradient system; Global attractor

Kategorie tematyczne

• 34D45: Attractors
• 47H20: Semigroups of nonlinear operators
• 37B25: Lyapunov functions and stability; attractors, repellers

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2009
• Tom: 7
• Numer: 3
• Strony: 487-492

Daty

wydano

2009-09-01

online

2009-08-12

Twórcy

autor

Vittorino Pata

• Politecnico di Milano

Bibliografia

• [1] Babin A.V., Vishik M.I., Attractors of evolution equations, North-Holland, Amsterdam, 1992
• [2] Chepyzhov V.V., Vishik M.I., Attractors for equations of mathematical physics, Amer. Math. Soc., Providence, 2002
• [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
• [4] Hale J.K., Asymptotic behavior of dissipative systems, Amer. Math. Soc., Providence, 1988
• [5] Haraux A., Systèmes dynamiques dissipatifs et applications, Masson, Paris, 1991
• [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
• [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
• [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
• [9] Robinson J.C., Infinite-dimensional dynamical systems, Cambridge University Press, Cambridge, 2001
• [10] Sell G.R., You Y., Dynamics of evolutionary equations, Springer, New York, 2002
• [11] Temam R., Infinite-dimensional dynamical systems in mechanics and physics, Springer, New York, 1997

Identyfikatory

DOI

10.2478/s11533-009-0034-3