The theory and applications of infinite dimensional dynamical systems have attracted the attention of scientists for quite some time. Dynamical issues arise in equations which attempt to model phenomena that change with time, and the infinite dimensional aspects occur when forces that describe the motion depend on spatial variables. This book may serve as an entree for scholars beginning their journey into the world of dynamical systems, especially infinite dimensional spaces. The main approach involves the theory of evolutionary equations. It begins with a brief essay on the evolution of evolutionary equations and introduces the origins of the basic elements of dynamical systems, flow and semiflow.
From the reviews:
"The book under review is a fundamental introduction into the field of infinite-dimensional dynamical systems, especially those generated from evolutionary partial differential equations. It is addressed to all those who embark on their journey into this fascinating topic ... . the book is nicely written, there are given useful commentaries on all steps and to original and surrounding works. It can be highly recommended to all those who wish to enjoy the world of dynamics of evolutionary equations." (J. Synnatzschke, Zeitschrift fur Analysis und ihre Anwendungen, Vol. 21 (3), 2002)
"The dynamics of evolutionary equations are a nice example of the interaction between the theory of ordinary and of partial differential equations. The present volume is a significant contribution to this theory, and should become soon a reference book. ... The book can undoubtedly be recommended and used as a basis for graduate courses in partial differential equations, as well as a reference volume for researchers in the important area of evolutionary equations." (Jean Mawhin, Bulletin of the Belgian Mathematical Society, Vol. 11 (4), 2004)
"Two well-known experts are the authors of this book on the theory and applications of infinite dimensional dynamical systems. ... Some basic results from functional analysis are included in the Appendices. This makes the book self-contained. ... The whole text is very carefully written. This excellent book will be certainly a basic reference on infinite dimensional dynamical systems. I can recommend it to researchers and graduate students in mathematics, physical sciences, and engineering." (Tibor Krisztin, Acta Scientiarum Mathematicarum, Vol. 69, 2003)
"The present book gives an introduction to infinite-dimensional dynamical systems suitable for graduate students with a solid background from functional analysis. ... It is well-written and contains many results which are otherwise hard to find in the text book literature." (G. Teschl, Monatshefte fur Mathematik, Vol. 138 (3), 2003)