Ladyzhenskaya, Olga Attractors for semigroups and evolution equations. (English) Zbl 0755.47049 Lezioni Lincee. Cambridge etc.: Cambridge University Press,. xi, 73 p. (1991). In these lecture notes the asymptotic behavior of a semigroup of nonlinear operators on a metric space is studied. The main objective is to establish the existence of a compact minimal global attractor (or \(B\)- attractor) and to estimate its Hausdorff and fractal dimension.In the first part of the book the theory is developed for semigroups of compact operators and asymptotically compact semigroups.Concrete semi-linear evolution equations are studied in the second part. A short section is devoted to the Navier-Stokes equation. Here a recent estimate (due to the author) of the fractal dimension and the number of determining modes is presented.The principal applications concern hyperbolic equations. For them, the entire program presented in the first part, is developed.The book permits, on a few pages, to get a quick access to some important topics of dynamic systems including, in particular, the detailed treatment of interesting concrete models. Reviewer: W.Arendt (Besançon) Cited in 4 ReviewsCited in 245 Documents MSC: 47H20 Semigroups of nonlinear operators 35B40 Asymptotic behavior of solutions to PDEs 47-02 Research exposition (monographs, survey articles) pertaining to operator theory 58-02 Research exposition (monographs, survey articles) pertaining to global analysis 35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations 47D06 One-parameter semigroups and linear evolution equations Keywords:asymptotic behavior of a semigroup of nonlinear operators on a metric space; existence of a compact minimal global attractor; \(B\)-attractor; estimate the Hausdorff and fractal dimension; semigroups of compact operators; asymptotically compact semigroups; semi-linear evolution equations; Navier-Stokes equation; hyperbolic equations PDFBibTeX XMLCite \textit{O. Ladyzhenskaya}, Attractors for semigroups and evolution equations. Cambridge etc.: Cambridge University Press (1991; Zbl 0755.47049)