One-Parameter Semigroups for Linear Evolution Equations (Graduate Texts in Mathematics (194))

I guess that, besides the classic references from Pazy and Jerome Goldstein, this title outstands in its category. I've heard several words of criticism over Pazy's work due to the lack of applications and several laments over the fact that Goldstein's book is out of print. This book introduces the semigroup theory like no other: it doesn't forget the historic and philosophical aspect of subject and it's full filled with applications and deep beauty. Congrats to the authors and also to the customers that decide to buy this title, may it be PDE or Dinamic Systems, you'll be home free... "This book gives an up-to-date account of the theory of strongly continuous one-parameter semigroups of linear operators. It includes a systematic discussion of the spectral theory and the long-term behavior of such semigroups. A special feature of the text is an unusually wide range of applications, to ordinary and partial differential operators, delay and Volterra equations and to control theory, et cetera, and an emphasis on philosophical motivation and the historical background."--BOOK JACKET. "The book is written for students, but should also be of value for researchers interested in this field."--BOOK JACKET. Linear evolution equations form an important part of operator theory. Such equations can be used to describe types of growth, for example cell growth or the growth of a population. This book gives an up-to-date account of the theory of one-parameter semigroups of linear evolution equations. The author emphasizes philosophical, mathematical, and historical motivation of the material, and the book will be useful for those interested in the theory and applications of semigroups. This book explores the theory of strongly continuous one-parameter semigroups of linear operators. A special feature of the text is an unusually wide range of applications such as to ordinary and partial differential operators, to delay and Volterra equations, and to control theory. Also, the book places an emphasis on philosophical motivation and the historical background. There are many good reasons-the reader may consult Section 1 of the Epilogue for details-why an "autonomous deterministic system" should be described by maps T(t), t 0, satisfying the functional equation (FE) T(t + s) = T(t)T(s).