Chueshov, I. D. Introduction to the theory of infinite-dimensional dissipative systems. (Vvedenie v teoriyu beskonechnomernykh dissipativnykh sistem.) (Russian) Zbl 1100.37046 Universitetskie Lektsii po Sovremennoj Matematike. Khar’kov: AKTA (ISBN 966-7021-23-8/hbk). 436 p. (1999). This textbook gives a systematic introduction to the main ideas, methods and problems of the mathematical theory of infinite-dimensional dissipative dynamical systems. The main attention is paid to systems generated by nonlinear partial differential equations arising in the modern mechanics. For the inspection of the table of contents see the review below to the English edition. Reviewer: Mikhail P. Moklyachuk (Kyïv) Cited in 95 Documents MSC: 37Lxx Infinite-dimensional dissipative dynamical systems 37-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to dynamical systems and ergodic theory 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs 70G60 Dynamical systems methods for problems in mechanics 35Q99 Partial differential equations of mathematical physics and other areas of application 74K20 Plates 74H99 Dynamical problems in solid mechanics 82B40 Kinetic theory of gases in equilibrium statistical mechanics 82D05 Statistical mechanics of gases Keywords:dissipative dynamical system; attractor; stability; invariant set; reduction principle; semilinear parabolic equation; Lyapunov function; nonlinear diffusion; model of turbulence; fluid; inertial manifold; nonlinear oscillations; supersonic gas PDFBibTeX XMLCite \textit{I. D. Chueshov}, Vvedenie v teoriyu beskonechnomernykh dissipativnykh sistem (Russian). Khar'kov: AKTA (1999; Zbl 1100.37046)