R. Tyrrell Rockafellar

Fabio Ancona

Henry Hermes

The aim of this volume is to provide a synthetic account of past research, to give an up-to-date guide to current intertwined developments of control theory and nonsmooth analysis, and also to point to future research directions.

In Honor of the 73rd Birthday of H. Hermes and of the 71st Birthday of R.T. Rockafellar

Geometric Control and Nonsmooth Analysis

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.

Fabio Ancona

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