An Introduction to Semiflows

Norbert J. Koksch

ISBN 10: 0367454289 / ISBN 13: 9780367454289

Published by Chapman And Hall/CRC, 2019

About this Item

nach der Bestellung gedruckt Neuware - Printed after ordering - 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.

Seller Inventory # 9780367454289

Bibliographic Details

• Title: An Introduction to Semiflows
• Publisher: Chapman And Hall/CRC
• Publication Date: 2019
• Language: English
• ISBN 10: 0367454289
• ISBN 13: 9780367454289
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 229W x 152H x 22D millimeters 229 millimeters width by 152 millimeters height by 22 millimeters depth
• Weight: 583 grams

About this title

Synopsis

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.

About the Author

Albert J. Milani is a professor in the Department of Mathematics, University of Wisconsin-Milwaukee, USA.

Norbert J. Koksch is a docent in the Department of Mathematics, Technische Universität, Dresden, Germany