Semigroups Associated with Dissipative Systems: 398 (Chapman & Hall/CRC Research Notes in Mathematics Series) - Softcover

Liu, Z; Zheng, Songmu

Softcover

ISBN 10: 0849306159 ISBN 13: 9780849306150

Publisher: Chapman and Hall/CRC, 1999

Synopsis

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.

About this title

Review

"The book is clearly written and recommended especially for researchers and graduate students in the field of functional analysis, partial differential equations and control theory." -Reinhard Racke, Mathematical Reviews

Edition details

• Publisher: Chapman and Hall/CRC
• Publication date: 1999
• ISBN 10: 0849306159
• ISBN 13: 9780849306150
• Binding: Paperback
• Language: English
• Edition number: 1
• Number of pages: 224