Semigroups for Delay Equations

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.

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.

Autorentext
Batkai, Andras; Piazzera, Susanna

Inhalt
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