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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.

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
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