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 hyperb 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.
Asymptotic stabilization of systems of conservation laws by controls acting at a single boundary point by F. Ancona and A. Marson Variational principles for finite-dimensional initial value problems by G. Auchmuty Boundary and localized null controllability of structurally damped elastic systems by G. Avalos and P. Cokeley Nonlinear aeroelastic theory: Continuum models by A. V. Balakrishnan Stability issues in the Euler-Korteweg model by S. Benzoni-Gavage, R. Danchin, S. Descombes, and D. Jamet Optimality conditions for solutions to hyperbolic balance laws by A. Bressan and W. Shen Long-time dynamics of a semilinear wave equation with nonlinear interior/boundary damping and sources of critical exponents by I. Chueshov and I. Lasiecka On the $p$-system at a junction by R. M. Colombo and M. Garavello Analyticity of stable invariant manifolds of 1D-semilinear parabolic equations by A. V. Fursikov Boundary feedback stabilization of nonlinear beam models by G. Hegarty and S. Taylor Increased stability in the continuation for the Helmholtz equation with variable coefficient by V. Isakov Microscale sensitivity in moving-boundary problems for the thin-film equation by J. R. King The heat and Schrodinger equations: Boundary control with one shot by W. Littman and S. Taylor A remark on the Morrey potential by J. Serrin Nonlinear dissipative wave equations with potential by G. Todorova and B. Yordanov Pointwise Carleman estimates, global uniqueness, observability, and stabilization for Schrodinger equations on Riemannian manifolds at the $H^1(\Omega)$-level by R. Triggiani and X. Xu.