Semigroups for Delay Equations

Batkai, Andras; Piazzera, Susanna

" "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"

• 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