**Contemporary Mathematics**

Volume: 426;
2007;
404 pp;
Softcover

MSC: Primary 35; 49; 93;

Print ISBN: 978-0-8218-3766-5

Product Code: CONM/426

List Price: $112.00

Individual Member Price: $89.60

**Electronic ISBN: 978-0-8218-8105-7
Product Code: CONM/426.E**

List Price: $112.00

Individual Member Price: $89.60

# Control Methods in PDE-Dynamical Systems

Share this page *Edited by *
*Fabio Ancona; Irena Lasiecka; Walter Littman; Roberto Triggiani*

While rooted in controlled PDE systems, this 2005 AMS-IMS-SIAM Summer Research Conference sought to reach out to a rather distinct, yet scientifically related, research community in mathematics interested in PDE-based dynamical systems. Indeed, this community is also involved in the study of dynamical properties and asymptotic long-time behavior (in particular, stability) of PDE-mixed problems. It was the editors' conviction that the time had become ripe and the circumstances propitious for these two mathematical communities—that of PDE control and optimization theorists and that of dynamical specialists—to come together in order to share recent advances and breakthroughs in their respective disciplines. This conviction was further buttressed by recent discoveries that certain energy methods, initially devised for control-theoretic a-priori estimates, once combined with dynamical systems techniques, yield wholly new asymptotic results on well-established, nonlinear PDE systems, particularly hyperbolic and Petrowski-type PDEs.

These expectations are now particularly well reflected in the contributions to this volume, which involve nonlinear parabolic, as well as hyperbolic, equations and their attractors; aero-elasticity, elastic systems; Euler-Korteweg models; thin-film equations; Schrodinger equations; beam equations; etc. In addition, the static topics of Helmholtz and Morrey potentials are also prominently featured. A special component of the present volume focuses on hyperbolic conservation laws, to take advantage of recent theoretical advances with significant implications also on applied problems. In all these areas, the reader will find state-of-the-art accounts as stimulating starting points for further research.

#### Table of Contents

# Table of Contents

## Control Methods in PDE-Dynamical Systems

- Contents v6 free
- Preface vii8 free
- Asymptotic Stabilization of Systems of Conservation Laws by Controls Acting at a Single Boundary Point 110 free
- Variational Principles for Finite Dimensional Initial Value Problems 4554
- Boundary and Localized Null Controllability of Structurally Damped Elastic Systems 5766
- Nonlinear Aeroelasticity Theory: Continuum Models 7988
- Stability Issues in the Euler-Korteweg Model 103112
- Optimality Conditions for Solutions to Hyperbolic Balance Laws 129138
- Long-Time Dynamics of a Semilinear Wave Equation with Nonlinear Interior/Boundary Damping and Sources of Critical Exponents 153162
- On the p-System at a Junction 193202
- Analyticity of Stable Invariant Manifolds of 1D-Semilinear Parabolic Equations 219228
- Boundary Feedback Stabilization of Nonlinear Beam Models 243252
- Increased Stability in the Continuation for the Helmholtz Equation with Variable Coefficient 255264
- Microscale Sensitivity in Moving-Boundary Problems for the Thin-Film Equation 269278
- The Heat and Schrödinger Equations: Boundary Control with One Shot 293302
- A Remark on the Morrey Potential 307316
- Nonlinear Dissipative Wave Equations with Potential 317326
- Pointwise Carleman Estimates, Global Uniqueness, Observability, and Stabilization for Schrödinger Equations on the Riemannian Manifolds at the H1(Ω)-Level 339348

#### Readership

Graduate students and research mathematicians interested in partial differential equations and control theory.