Pata, Vittorino; Zelik, Sergey A result on the existence of global attractors for semigroups of closed operators. (English) Zbl 1152.47046 Commun. Pure Appl. Anal. 6, No. 2, 481-486 (2007). The asymptotic behavior of semigroups is an interesting problems in differential equations and dynamical systems, as it explains the long-time behaviors of solutions. This paper deals with the existence of global attractors for nonlinear semigroups \(S(t)\), \(t\geq0\), of operators on Banach spaces under weaker conditions, namely, when \(S(t)\) is a closed map. The authors prove the existence of a global attractor when there is an absorbing set of \(S(t)\), \(t\geq0\). An application is given for some wave equations with nonlinear damping. Reviewer: Khalil Ezzinbi (Marrakech) Cited in 1 ReviewCited in 42 Documents MSC: 47H20 Semigroups of nonlinear operators 34D45 Attractors of solutions to ordinary differential equations 47J35 Nonlinear evolution equations 37L30 Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems Keywords:semigroups of operators; abstract Cauchy problem; closed operators; global attractors; absorbing sets PDFBibTeX XMLCite \textit{V. Pata} and \textit{S. Zelik}, Commun. Pure Appl. Anal. 6, No. 2, 481--486 (2007; Zbl 1152.47046) Full Text: DOI