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Zusatztext " ""The book describes the semigroup approach to delay equations in a well-arranged and understandable way. Moreover! it contains many references for different approaches to delay equations. Theoretical results are always followed by illustrative examples. Therefore! the book will be useful for graduate students as well as for researchers in evolution equations."" -Newsletter of the European Mathematical Society ! June 2006""With clear writing and multiple scientific or pedagogic examples! it is the opinion of this reviewer that the authors do a good job presenting a synthesis of a significant mass of work on the [subjects of semigroups and delay equations]."" -Mathematiacl Reviews! May 2006" Informationen zum Autor Batkai! Andras; Piazzera! Susanna Klappentext Presenting how delay equations can be studied in Lp-history spaces! this book contains appendices offering supplementary information; and also a comprehensive index. It is a useful research tool for mathematicians! chemists! biologists and economists. Zusammenfassung In most physical, chemical, biological and economic phenomena it is quite natural to assume that the system not only depends on the present state but also on past occurrences. These circumstances are mathematically described by partial differential equations with delay. This book presents, in a systematic fashion, how delay equations can be studied in Lp-history spaces. Appendices offering supplementary information and a comprehensive index make this book an ideal introduction and research tool for mathematicians, chemists, biologists and economists. Inhaltsverzeichnis Part I: Preliminary Results in Semigroup Theory 1. Semigroup Theory 2. Spectral Theory and Asymptotics of Semigroups Part II: Well-Posedness 3. The Delay Semigroup Part III: Asymptotic Behavior 4. Stability via Spectral Properties 5. Stability via Perturbation 6. Stability via Positivity 7. Small Delays 8. More Asymptotic Properties Part IV: More Delay Equations 9. Second-Order Cauchy Problems with Delay 10. Delays in the Highest-Order Derivatives ...
Summary
This book describes how to construct the solutions of the delay equation from the semigroup associated to the equivalent abstract Cauchy problem. It considers parabolic problems with delays in the highest order derivatives and discusses abstract delay equations on a Banach space.
