Control Methods in PDE-Dynamical Systems
About this Title
Fabio Ancona, Irena Lasiecka, Walter Littman and Roberto Triggiani, Editors
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.
Graduate students and research mathematicians interested in partial differential equations and control theory.
Table of Contents
- Fabio Ancona and Andrea Marson – Asymptotic stabilization of systems of conservation laws by controls acting at a single boundary point [MR 2311519]
- Giles Auchmuty – Variational principles for finite dimensional initial value problems [MR 2311520]
- George Avalos and Paul Cokeley – Boundary and localized null controllability of structurally damped elastic systems [MR 2311521]
- A. V. Balakrishnan – Nonlinear aeroelastic theory: continuum models [MR 2311522]
- Sylvie Benzoni-Gavage, Raphaël Danchin, Stéphane Descombes and Didier Jamet – Stability issues in the Euler-Korteweg model [MR 2311523]
- Alberto Bressan and Wen Shen – Optimality conditions for solutions to hyperbolic balance laws [MR 2311524]
- Igor Chueshov and Irena Lasiecka – Long-time dynamics of a semilinear wave equation with nonlinear interior/boundary damping and sources of critical exponents [MR 2311525]
- Rinaldo M. Colombo and Mauro Garavello – On the $p$-system at a junction [MR 2311526]
- A. V. Fursikov – Analyticity of stable invariant manifolds of 1D-semilinear parabolic equations [MR 2311527]
- Gareth Hegarty and Stephen Taylor – Boundary feedback stabilization of nonlinear beam models [MR 2311528]
- Victor Isakov – Increased stability in the continuation for the Helmholtz equation with variable coefficient [MR 2311529]
- J. R. King – Microscale sensitivity in moving-boundary problems for the thin-film equation [MR 2311530]
- Walter Littman and Stephen Taylor – The heat and Schrödinger equations: boundary control with one shot [MR 2311531]
- James Serrin – A remark on the Morrey potential [MR 2311532]
- Grozdena Todorova and Borislav Yordanov – Nonlinear dissipative wave equations with potential [MR 2311533]
- Roberto Triggiani and Xiangjin Xu – Pointwise Carleman estimates, global uniqueness, observability, and stabilization for Schrödinger equations on Riemannian manifolds at the $H^1(\Omega )$-level [MR 2311534]