An introduction to semiflows

Author(s)

• Milani, Albert
• Koksch, Norbert J.

Bibliographic Information

An introduction to semiflows

Albert J. Milani, Norbert J. Koksch

（Chapman & Hall/CRC monographs and surveys in pure and applied mathematics, 134）

Chapman & Hall/CRC, c2005

Note

Includes bibliographical references and index

Description and Table of Contents

Description

This book introduces the class of dynamical systems called semiflows, which includes systems defined or modeled by certain types of differential evolution equations (DEEs). It focuses on the basic results of the theory of dynamical systems that can be extended naturally and applied to study the asymptotic behavior of the solutions of DEEs. The authors concentrate on three types of absorbing sets: attractors, exponential attractors, and inertial manifolds. They present the fundamental properties of these sets, and then proceed to show the existence of some of these sets for a number of dynamical systems generated by well-known physical models. In particular, they consider in full detail two particular PDEEs: a semilinear version of the heat equation and a corresponding version of the dissipative wave equation. These examples illustrate the most important features of the theory of semiflows and provide a sort of template that can be applied to the analysis of other models. The material builds in a careful, gradual progression, developing the background needed by newcomers to the field, and culminating in a more detailed presentation of the main topics than found in most sources. The authors' approach to and treatment of the subject builds the foundation for more advanced references and research on global attractors, exponential attractors, and inertial manifolds.

Table of Contents

Dynamical Processes. Attractors of Semiflows. Attractors for Semilinear Evolution Equations. Exponential Attractors. Inertial Manifolds. Examples. A Non-Existence Result for Inertial Manifolds. Appendix: Selected Results from Analysis. Bibliography. Index. Nomenclature

by "Nielsen BookData"

Details

• NCID: BA69676827
• ISBN:
  • 1584884584
• LCCN: 2004055145
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Boca Raton, Fla.
• Pages/Volumes: xvi, 386 p.
• Size: 25 cm
• Classification:
  • LCC : QA614.82
  • DC22 : 515/.352
• Subject Headings:
  • LCSH : Flows (Differentiable dynamical systems)
• Parent Bibliography ID:
  • BA41758925