Semigroups Associated with Dissipative Systems

1st Edition

Z Liu, Songmu Zheng

Chapman and Hall/CRC
Published January 29, 1999
Reference - 224 Pages
ISBN 9780849306150 - CAT# LM0615
Series: Chapman & Hall/CRC Research Notes in Mathematics Series

For Instructors Request Inspection Copy

USD$180.00

Add to Wish List
FREE Standard Shipping!

Summary

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.

Instructors

We provide complimentary e-inspection copies of primary textbooks to instructors considering our books for course adoption.

Request an
e-inspection copy

Share this Title