Semigroups associated with dissipative systems
著者
書誌事項
Semigroups associated with dissipative systems
(Research notes in mathematics, 398)
Chapman & Hall/CRC, c1999
- : pbk
大学図書館所蔵 全45件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Includes bibliographical references (p. 191-203) and index
内容説明・目次
内容説明
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.
目次
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
「Nielsen BookData」 より