On the theory of global attractors and Lyapunov functionals
type: Item
instance of: scholarly article
title: On the theory of global attractors and Lyapunov functionals
zbMATH Open document ID: 1260.37048
author: Michele Coti Zelati
published in: Set-Valued and Variational Analysis
publication date: 2013-02-21T00:00:00Z
review text: This work is devoted to the study of the existence of global attractors for multivalued and single-valued semigroups, more specifically, under which conditions a multivalued (or single-valued) semigroup \(\{S(t): t\geqslant 0\}\) possesses a global attractor \(\mathcal{A}\). The proofs are based on classical techniques of semigroups, making use of the Kuratowski measure of noncompactness and a condition of asymptotical compactness. Also, the author uses the results to prove the existence of an attractor for an equation ruling the evolution of the specific humidity in a system of moist air. Finally, using the proven results, the author gives a simple proof of the existence and the characterization of the global attractor of a Lyapunov single-valued semigroup as the unstable set of its equilibrium points.
reviewed by: Matheus Cheque Bortolan
Mathematics Subject Classification ID: 37L05
Mathematics Subject Classification ID: 47H04
Mathematics Subject Classification ID: 47H20
Mathematics Subject Classification ID: 37L45
zbMATH DE Number: 6138208
zbMATH Keywords: multivalued dynamical systems
zbMATH Keywords: global attractors
zbMATH Keywords: Lyapunov function
zbMATH Keywords: unstable set
zbMATH Keywords: stationary points
MaRDI profile type: Publication
full work available at URL: s11228-012-0215-2
OpenAlex ID: W1967157081
cites work: DYNAMICS OF A REACTION–DIFFUSION EQUATION WITH A DISCONTINUOUS NONLINEARITY
cites work: Set-valued analysis
cites work: Continuity properties and global attractors of generalized semiflows and the Navier-Stokes equations
cites work: Q4003101
cites work: Pullback attractors of nonautonomous and stochastic multivalued dynamical systems
cites work: A comparison between two theories for multi-valued semiflows and their asymptotic behaviour
cites work: A minimal approach to the theory of global attractors
cites work: Attractors for equations of mathematical physics
cites work: Evolution equations and their trajectory attractors
cites work: Weakly dissipative semilinear equations of viscoelasticity
cites work: Multivalued attractors and their approximation: applications to the Navier-Stokes equations
cites work: Regular global attractors of type III thermoelastic extensible beams
cites work: Some existence, uniqueness and nonuniqueness theorems for solutions of parabolic equations with discontinuous nonlinearities
cites work: On attractors for multivalued semigroups defined by generalized semiflows
cites work: On the extensible viscoelastic beam
cites work: Q4039920
cites work: Negatively invariant sets and entire trajectories of set-valued dynamical systems
cites work: Attractors of weakly asymptotically compact set-valued dynamical systems
cites work: Q3998731
cites work: New formulations of the primitive equations of atmosphere and applications
cites work: On attractors of multivalued semi-flows and differential inclusions
cites work: Addendum to ``On attractors of multivalued semiflows and differential inclusions'' [Set-valued Anal. 6, No.\,1, 83--111 (1998; Zbl 0915.58063)]
cites work: Gradient systems of closed operators
cites work: A result on the existence of global attractors for semigroups of closed operators
cites work: Introduction (to ``From finite to infinite dimensional dynamical systems'')
cites work: Attractors for gradient flows of nonconvex functionals and applications
cites work: Dynamics of evolutionary equations
cites work: Infinite-dimensional dynamical systems in mechanics and physics.
cites work: Navier-Stokes equations. Theory and numerical analysis. Repr. with corr
cites work: Attractors of parabolic equations without uniqueness
DOI: 10.1007/S11228-012-0215-2
description: scientific article; zbMATH DE number 6138208