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Differential Geometric Methods in the Control of Partial Differential Equations

Edited by: Robert Gulliver University of Minnesota, Minneapolis, MN
Walter Littman University of Minnesota, Minneapolis, MN
Roberto Triggiani University of Virginia, Charlottesville, VA
Available Formats:
Softcover ISBN: 978-0-8218-1927-2
Product Code: CONM/268
List Price: $102.00 MAA Member Price:$91.80
AMS Member Price: $81.60 Electronic ISBN: 978-0-8218-7858-3 Product Code: CONM/268.E List Price:$96.00
MAA Member Price: $86.40 AMS Member Price:$76.80
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List Price: $153.00 MAA Member Price:$137.70
AMS Member Price: $122.40 Click above image for expanded view Differential Geometric Methods in the Control of Partial Differential Equations Edited by: Robert Gulliver University of Minnesota, Minneapolis, MN Walter Littman University of Minnesota, Minneapolis, MN Roberto Triggiani University of Virginia, Charlottesville, VA Available Formats:  Softcover ISBN: 978-0-8218-1927-2 Product Code: CONM/268  List Price:$102.00 MAA Member Price: $91.80 AMS Member Price:$81.60
 Electronic ISBN: 978-0-8218-7858-3 Product Code: CONM/268.E
 List Price: $96.00 MAA Member Price:$86.40 AMS Member Price: $76.80 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$153.00 MAA Member Price: $137.70 AMS Member Price:$122.40
• Book Details

Contemporary Mathematics
Volume: 2682000; 406 pp
MSC: Primary 53; 35; 49; 93;

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.

Graduate students and research mathematicians interested in differential geometry.

• Articles
• George Avalos - Wellposedness of a structural acoustics model with point control [ MR 1804787 ]
• John Cagnol and Jean-Paul Zolésio - Intrinsic geometric model for the vibration of a constrained shell [ MR 1804788 ]
• Mehmet Camurdan and Guangcao Ji - A noise reduction problem arising in structural acoustics: a three-dimensional solution [ MR 1804789 ]
• S. Chanillo, D. Grieser and K. Kurata - The free boundary problem in the optimization of composite membranes [ MR 1804790 ]
• Michel C. Delfour - Tangential differential calculus and functional analysis on a $C^{1,1}$ submanifold [ MR 1804791 ]
• Matthias M. Eller and Victor Isakov - Carleman estimates with two large parameters and applications [ MR 1804792 ]
• José F. Escobar - On the prescribed scalar curvature problem on compact manifolds with boundary [ MR 1804793 ]
• Robert Gulliver and Walter Littman - Chord uniqueness and controllability: the view from the boundary. I [ MR 1804794 ]
• Mary Ann Horn - Nonlinear boundary stabilization of a system of anisotropic elasticity with light internal damping [ MR 1804795 ]
• Victor Isakov and Masahiro Yamamoto - Carleman estimate with the Neumann boundary condition and its applications to the observability inequality and inverse hyperbolic problems [ MR 1804796 ]
• I. Lasiecka, R. Triggiani and X. Zhang - Nonconservative wave equations with unobserved Neumann B.C.: global uniqueness and observability in one shot [ MR 1804797 ]
• Catherine Lebiedzik - Uniform stability of a coupled structural acoustic system with thermoelastic effects and weak structural damping [ MR 1804798 ]
• Tomasz Lewiński and Jan Sokołowski - Topological derivative for nucleation of non-circular voids. The Neumann problem [ MR 1804799 ]
• Walter Littman - Remarks on global uniqueness theorems for partial differential equations [ MR 1804800 ]
• Zbigniew Slodkowski and Giuseppe Tomassini - Evolution of a graph by Levi form [ MR 1804801 ]
• Peng-Fei Yao - Observability inequalities for the Euler-Bernoulli plate with variable coefficients [ MR 1804802 ]
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Volume: 2682000; 406 pp
MSC: Primary 53; 35; 49; 93;

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.

Graduate students and research mathematicians interested in differential geometry.

• Articles
• George Avalos - Wellposedness of a structural acoustics model with point control [ MR 1804787 ]
• John Cagnol and Jean-Paul Zolésio - Intrinsic geometric model for the vibration of a constrained shell [ MR 1804788 ]
• Mehmet Camurdan and Guangcao Ji - A noise reduction problem arising in structural acoustics: a three-dimensional solution [ MR 1804789 ]
• S. Chanillo, D. Grieser and K. Kurata - The free boundary problem in the optimization of composite membranes [ MR 1804790 ]
• Michel C. Delfour - Tangential differential calculus and functional analysis on a $C^{1,1}$ submanifold [ MR 1804791 ]
• Matthias M. Eller and Victor Isakov - Carleman estimates with two large parameters and applications [ MR 1804792 ]
• José F. Escobar - On the prescribed scalar curvature problem on compact manifolds with boundary [ MR 1804793 ]
• Robert Gulliver and Walter Littman - Chord uniqueness and controllability: the view from the boundary. I [ MR 1804794 ]
• Mary Ann Horn - Nonlinear boundary stabilization of a system of anisotropic elasticity with light internal damping [ MR 1804795 ]
• Victor Isakov and Masahiro Yamamoto - Carleman estimate with the Neumann boundary condition and its applications to the observability inequality and inverse hyperbolic problems [ MR 1804796 ]
• I. Lasiecka, R. Triggiani and X. Zhang - Nonconservative wave equations with unobserved Neumann B.C.: global uniqueness and observability in one shot [ MR 1804797 ]
• Catherine Lebiedzik - Uniform stability of a coupled structural acoustic system with thermoelastic effects and weak structural damping [ MR 1804798 ]
• Tomasz Lewiński and Jan Sokołowski - Topological derivative for nucleation of non-circular voids. The Neumann problem [ MR 1804799 ]
• Walter Littman - Remarks on global uniqueness theorems for partial differential equations [ MR 1804800 ]
• Zbigniew Slodkowski and Giuseppe Tomassini - Evolution of a graph by Levi form [ MR 1804801 ]
• Peng-Fei Yao - Observability inequalities for the Euler-Bernoulli plate with variable coefficients [ MR 1804802 ]
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