Differential Geometric Methods In The Control Of Partial Differential Equations
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Differential Geometric Methods in the Control of Partial Differential Equations
Author: Robert Gulliver
language: en
Publisher: American Mathematical Soc.
Release Date: 2000
This volume contains selected papers that were presented at the AMS-IMS-SIAM Joint Summer Research Conference on "Differential Geometric Methods in the Control of Partial Differential Equations", which was held at the University of Colorado in Boulder in June 1999. The aim of the conference was to explore the infusion of differential-geometric methods into the analysis of control theory of partial differential equations, particularly in the challenging case of variable coefficients, where the physical characteristics of the medium vary from point to point. While a mutually profitable link has been long established, for at least 30 years, between differential geometry and control of ordinary differential equations, a comparable relationship between differential geometry and control of partial differential equations (PDEs) is a new and promising topic. Very recent research, just prior to the Colorado conference, supported the expectation that differential geometric methods, when brought to bear on classes of PDE modelling and control problems with variable coefficients, will yield significant mathematical advances. The papers included in this volume - written by specialists in PDEs and control of PDEs as well as by geometers - collectively support the claim that the aims of the conference are being fulfilled. In particular, they endorse the belief that both subjects-differential geometry and control of PDEs-have much to gain by closer interaction with one another. Consequently, further research activities in this area are bound to grow.
Geometric Methods in Inverse Problems and PDE Control
Author: Chrisopher B. Croke
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
This IMA Volume in Mathematics and its Applications GEOMETRIC METHODS IN INVERSE PROBLEMS AND PDE CONTROL contains a selection of articles presented at 2001 IMA Summer Program with the same title. We would like to thank Christopher B. Croke (University of Penn sylva nia), Irena Lasiecka (University of Virginia), Gunther Uhlmann (University of Washington), and Michael S. Vogelius (Rutgers University) for their ex cellent work as organizers of the two-week summer workshop and for editing the volume. We also take this opportunity to thank the National Science Founda tion for their support of the IMA. Series Editors Douglas N. Arnold, Director of the IMA Fadil Santosa, Deputy Director of the IMA v PREFACE This volume contains a selected number of articles based on lectures delivered at the IMA 2001 Summer Program on "Geometric Methods in Inverse Problems and PDE Control. " The focus of this program was some common techniques used in the study of inverse coefficient problems and control problems for partial differential equations, with particular emphasis on their strong relation to fundamental problems of geometry. Inverse coef ficient problems for partial differential equations arise in many application areas, for instance in medical imaging, nondestructive testing, and geophys ical prospecting. Control problems involving partial differential equations may arise from the need to optimize a given performance criterion, e. g. , to dampen out undesirable vibrations of a structure , or more generally, to obtain a prescribed behaviour of the dynamics.
Lecture Notes on Geometrical Aspects of Partial Differential Equations
Author: Viktor Viktorovich Zharinov
language: en
Publisher: World Scientific
Release Date: 1992
This book focuses on the properties of nonlinear systems of PDE with geometrical origin and the natural description in the language of infinite-dimensional differential geometry. The treatment is very informal and the theory is illustrated by various examples from mathematical physics. All necessary information about the infinite-dimensional geometry is given in the text.