Infinite-dimensional dynamical systems : an introduction to dissipative parabolic PDEs and the theory of global attractors / James C. Robinson

The book is written as a nice introduction to the – probably most complete nowadays monograph devoted to the theory of global attractors – Infinite-Dimensional Dynamical Systems in Mechanics and Physics by R. Temam and will undoubtedly be helpful for graduate students in their preliminary study of this subject. However, the book does not give a wider review of the recent approach to solvability of parabolic equations (related to D. Henry [Geometric theory of semilinear parabolic equations, Lecture Notes in Mathematics, 840 (1981; Zbl 0456.35001)]); the monographs by A. Pazy [Semigroups of linear operators and applications to partial differential equations, Applied Mathematical Sciences, 44, New York etc.: Springer-Verlag (1983; Zbl 0516.47023)], H. Amann [Linear and quasilinear parabolic problems, Vol. 1: Abstract linear theory, Monographs in Mathematics, 89, Basel: Birkhäuser (1995; Zbl 0819.35001)], A. Lunardi [Analytic semigroups and optimal regularity in parabolic problems, Progress in Nonlinear Differential Equations and their Applications, 16, Basel: Birkhäuser (1995; Zbl 0816.35001)] do not appear even in the references. Such an approach may also be important for students since it allows for the unified treatment of the existence of global attractors for a large class of parabolic equations and systems. (Zentralblatt)

Bibliogr. p. 445-452. Index