Control theory of partial differential equations

Guenter Leugering, Oleg Imanuvilov, Bing-Yu Zhang, Roberto Triggiani0824725468, 9780824725464, 9781420028317

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 :
Front Cover……Page 1
Preface……Page 8
Contributors……Page 10
Contents……Page 12
1. Asymptotic Rates of Blowup for the Minimal Energy Function for the Null Controllability of Thermoelastic Plates: The Free Case……Page 16
2. Interior and Boundary Stabilization of Navier-Stokes Equations……Page 44
3. On Approximating Properties of Solutions of the Heat Equation……Page 58
4. Kolmogorov’s ε-Entropy for a Class of Invariant Sets and Dimension of Global Attractors for Second-Order Evolution Equation……Page 66
5. Extension of the Uniform Cusp Property in Shape Optimization……Page 86
6. Garding’s Inequality on Manifolds with Boundary……Page 102
7. An Inverse Problem for the Dynamical Lame System with Two Sets of Local Boundary Data……Page 116
8. On Singular Perturbations in Problems of Exact Controllability of Second-Order Control Systems……Page 126
9. Domain Decomposition in Optimal Control Problems for Partial Differential Equations Revisited……Page 140
10. Controllability of Parabolic and Hyperbolic Equations: Toward a Unified Theory……Page 172
11. A Remark on Boundary Control on Manifolds……Page 190
12. Model Structure and Boundary Stabilization of an Axially Moving Elastic Tape……Page 198
13. Nonlinear Perturbations of Partially Controllable Systems……Page 210
14. On Junctions in a Network of Canals……Page 222
15. On Uniform Null Controllability and Blowup Estimates……Page 228
16. Poroelastic Filtration Coupled to Stokes Flow……Page 244
17. Operator-Valued Analytic Functions Generated by Aircraft Wing Model (Subsonic Case)……Page 258
18. Optimal Design of Mechanical Structures1……Page 274
19. Global Exact Controllability on H1Γ0(Ω)× L2(Ω) of Semilinear Wave Equations with NeumannL2 (0, T; L2(Γ1))-Boundary Control……Page 288
20. Carleman Estimates for the Three-Dimensional Nonstationary Lame System and Application to an Inverse Problem……Page 352
21. Forced Oscillations of a Damped Benjamin-Bona-Mahony Equation in a Quarter Plane……Page 390
22. Exact Controllability of the Heat Equation with Hyperbolic Memory Kernel……Page 402