A result on the existence of global attractors for semigroups of closed operators. (English) Zbl 1152.47046
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)
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 |