Control Theory of Partial Differential Equations

by Leugering; Guenter

• ISBN13: 9780824725464
• ISBN10: 0824725468
• Format: Nonspecific Binding
• Copyright: 2005-05-27
• Publisher: Chapman & Hall/

Summary

The field of control theory in PDEs has broadened considerably as more realistic models have been introduced and investigated. This book presents a broad range of recent developments, new discoveries, and mathematical tools in the field. The authors discuss topics such as elasticity, thermo-elasticity, aero-elasticity, interactions between fluids and elastic structures, and fluid dynamics and the new challenges that they present. Other control theoretic problems include parabolic systems, dynamical Lame systems, linear and nonlinear hyperbolic equations, and pseudo-differential operators on a manifold. This is a valuable tool authored by international specialists in the field.

Table of Contents

Preface	vii
Contributors	ix
Asymptotic Rates of Blowup for the Minimal Energy Function for the Null Controllability of Thermoelastic Plates: The Free Case	1	(28)
George Avalos
Irena Lasiecka
Interior and Boundary Stabilization of Navier-Stokes Equations	29	(14)
Viorel Barbu
On Approximating Properties of Solutions of the Heat Equation	43	(8)
Mikhail I. Belishev
Kolmogorov's ε-Entropy for a Class of Invariant Sets and Dimension of Global Attractors for Second-Order Evolution Equations with Nonlinear Damping	51	(20)
Igor Chueshov
Irena Lasiecka
Extension of the Uniform Cusp Property in Shape Optimization	71	(16)
Michel C. Delfour
Nicolas Doyon
Jean-Paul Zolesio
Garding's Inequality on Manifolds with Boundary	87	(14)
Matthias M. Eller
An Inverse Problem for the Dynamical Lame System with Two Sets of Local Boundary Data	101	(10)
Victor Isakov
On Singular Perturbations in Problems of Exact Controllability of Second-Order Control Systems	111	(14)
Jack E. Lagnese
Domain Decomposition in Optimal Control Problems for Partial Differential Equations Revisited	125	(32)
Guenter Leugering
Controllability of Parabolic and Hyperbolic Equations: Toward a Unified Theory	157	(18)
Wei Li
Xu Zhang
A Remark on Boundary Control on Manifolds	175	(8)
Walter Littman
Model Structure and Boundary Stabilization of an Axially Moving Elastic Tape	183	(12)
Zhuangyi Liu
David L. Russell
Nonlinear Perturbations of Partially Controllable Systems	195	(12)
Michael Renardy
On Junctions in a Network of Canals	207	(6)
E.J.P. Georg Schmidt
On Uniform Null Controllability and Blowup Estimates	213	(16)
Thomas I. Seidman
Poroelastic Filtration Coupled to Stokes Flow	229	(14)
Ralph E. Showalter
Operator-Valued Analytic Functions Generated by Aircraft Wing Model (Subsonic Case)	243	(16)
Marianna A. Shubov
Optimal Design of Mechanical Structures	259	(14)
Jurgen Sprekels
Dan Tiba
Global Exact Controllability on H1Γ0 (Omega;) x L2(Ω) of Semilinear Wave Equations with Neumann L2(0,T; L2(T1))-Boundary Control	273	(64)
Roberto Triggiani
Carleman Estimates for the Three-Dimensional Nonstationary Lame System and Application to an Inverse Problem	337	(38)
Oleg Imanuvilov
Masahiro Yamamoto
Forced Oscillations of a Damped Benjamin-Bona-Mahony Equation in a Quarter Plane	375	(12)
Yiming Yang
Bing-Yu Zhang
Exact Controllability of the Heat Equation with Hyperbolic Memory Kernel	387
Jiongmin Yong
Xu Zhang