Semigroups associated with dissipative systems

Author(s)

• Liu, Zhuangyi
• Zheng, S. (Songmu)

Bibliographic Information

Semigroups associated with dissipative systems

Zhuangyi Liu, Songmu Zheng

（Research notes in mathematics, 398）

Chapman & Hall/CRC, c1999

• : pbk

Note

Includes bibliographical references (p. 191-203) and index

Description and Table of Contents

Description

Motivated by applications to control theory and to the theory of partial differential equations (PDE's), the authors examine the exponential stability and analyticity of C0-semigroups associated with various dissipative systems. They present a unique, systematic approach in which they prove exponential stability by combining a theory from semigroup theory with partial differential equation techniques, and use an analogous theorem with PDE techniques to prove analyticity. The result is a powerful but simple tool useful in determining whether these properties will preserve for a given dissipative system. The authors show that the exponential stability is preserved for all the mechanical systems considered in this book-linear, one-dimensional thermoelastic, viscoelastic and thermoviscoelastic systems, plus systems with shear or friction damping. However, readers also learn that this property does not hold true for linear three-dimensional systems without making assumptions on the domain and initial data, and that analyticity is a more sensitive property, not preserved even for some of the systems addressed in this study.

Table of Contents

Preliminaries Some Definitions C0-Semigroup Generated by Dissipative Operator Exponential Stability and Analyticity The Sobolev Spaces and Elliptic Boundary Value Problems Linear Thermoelastic Systems The Setting of Problems for the One-Dimensional Thermoelastic System The Exponential Stability for the Dirichlet Boundary Conditions at Both Ends The Exponential Stability for the Stress-Free Boundary Conditions at Both Ends The Exponential Stability for the Stress-Free Boundary Conditions at One End The Thermoelastic Kirchhoff Plate Equations Linear Viscoelastic System Linear Viscoelastic System Wave Equation with Locally Distributed Damping Linear Viscoelastic System with Memory The Linear Viscoelastic Kirchoff Plate with Memory Linear Thermoviscoelastic Systems Linear One-Dimensional Thermoviscoelastic System Linear Three-Dimensional Thermoviscoelastic System with Memory Elastic Systems with Shear Damping Shear Diffusion Equations Laminated Beam with Shear Damping Linear Elastic Systems with Boundary Damping Second-Order Hyperbolic Equation Euler-Bernoulli Beam Equation Uniformly Stable Approximations Main Theorem Approximations of the Thermoelastic System Approximation of the Viscoelastic System Bibliography

by "Nielsen BookData"

Details

• NCID: BA41924208
• ISBN:
  • 0849306159
• LCCN: 98051412
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Boca Raton
• Pages/Volumes: 206 p.
• Size: 24 cm
• Classification:
  • LCC : QA808
  • DC21 : 512/.2
• Subject Headings:
  • LCSH : Mechanics, Analytic
  • LCSH : Semigroups
• Parent Bibliography ID:
  • BA41222266