On the theory of global attractors and Lyapunov functionals (Q1938517)

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.