Control Theory of Partial Differential Equations

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.

Guenter Leugering, University of Erlangen, Nuremberg, Germany. Oleg Imanuvilov, Iowa State University, Ames, Iowa, USA. Bing-Yu Zhang, University of Cincinnati, Cincinnati, Ohio, USA. Roberto Triggiani, University of Virginia, Charlottesville, Virginia, USA.

Preface 1 Asymptotic Rates of Blowup for the Minimal Energy Function for the Null Controllability of Thermoelastic Plates: The Free Case 2 Interior and Boundary Stabilization of Navier-Stokes Equations 3 On Approximating Properties of Solutions of the Heat Equation 4 Kolmogorov's ?-Entropy for a Class of Invariant Sets and Dimension of Global Attractors for Second-Order Evolution Equations with Nonlinear Damping 5 Extension of the Uniform Cusp Property in Shape Optimization 6 Garding ? 's Inequality on Manifolds with Boundary 7 An Inverse Problem for the Dynamical Lame System with Two Sets of Local Boundary Data 8 On Singular Perturbations in Problems of Exact Controllability of Second-Order Control Systems 9 Domain Decomposition in Optimal Control Problems for Partial Differential Equations Revisited 10 Controllability of Parabolic and Hyperbolic Equations: Toward a Unified Theory 11 A Remark on Boundary Control on Manifolds. 12 Model Structure and Boundary Stabilization of an Axially Moving Elastic Tape 13 Nonlinear Perturbations of Partially Controllable Systems 14 On Junctions in a Network of Canals 15 On Uniform Null Controllability and Blowup Estimates 16 Poroelastic Filtration Coupled to Stokes Flow 17 Operator-Valued Analytic Functions Generated by Aircraft Wing Model (Subsonic Case) 18 Optimal Design of Mechanical Structures 19 Global Exact Controllability on H1 (?) × L2(?) of Semilinear Wave Equations with Neumann L2(0,T;L2(?1))-Boundary Control 20 Carleman Estimates for the Three-Dimensional Nonstationary Lame- System and Application to an Inverse Problem 21 Forced Oscillations of a Damped Benjamin-Bona-Mahony Equation in a Quarter Plane 22 Exact Controllability of the Heat Equation with Hyperbolic Memory Kernel