This volume contains a selection of articles based on lectures delivered at the IMA 2001 Summer Program on Geometric Methods in Inverse Problems and PDE Control. The articles are focused around a set of common tools used in the study of inverse coefficient and control problems for PDEs and related differential geometric problems. This book will serve as an excellent starting point for researchers wanting to pursue studies at the intersection of these mathematically exciting and practically important subjects.
Geometric Methods in Inverse Problems and PDE Control
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This volume contains a slected number of articles based on lectures delivered at the IMA 2001 Summer Program on Geometric Methods in Inverse Problems and PDE Control. This program was focused on a set of common tools that are used in the study of inverse coefficient problems and control problems for partial differential equations, and in particular on their strong relation to fundamental problems of differential geometry. Examples of such tools are Dirichlet-to-Neumann data boundary maps, unique continuation results, Carleman estimates, microlocal analysis and the so-called boundary control method. Examples of intimately connected fundamental problems in differential geometry are the boundary rigidity problem and the isospectral problem. The present volume provides a broad survey of recent progress concerning inverse and control problems for PDEs and related differential geometric problems. It is hoped that it will also serve as an excellent ``point of departure" for researchers who will want to pursue studies at the intersection of these mathematically exciting, and practically important subjects.
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Inside This Book
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First Sentence:
Let M be a closed Riemannian manifold. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
positive second fundamental form, analytic plane domains, chord uniqueness, following continuous observability inequality, bouncing ball orbit, boundary rigidity problem, boundary distance function, isospectral metrics, energy method approach, cutoff operator, insulating cracks, wave invariants, wave trace invariants, ghost orbits, pseudoconvex with respect, sharp trace regularity, outward normal field, unique continuation result, conducting cracks, marked length spectrum, scattering relation, geodesic fibers, strong unique continuation, observability inequalities, real principal symbol Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Pure Appl, Euclidean Laplacian, Siberian Math, Lecture Notes, Annals of Math, Gunther Uhlmann, Springer Verlag, Contemporary Mathematics, Matrix Riccati Comparison Theorem, Applied Mathematics, Inverse Prohl, Michael Vogelius, Marcel Dekker, National Science Foundation, New Geom, Pure Math, Pures Appl, Rio de Janeiro, Springer Lect, University of Virginia New!
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Let M be a closed Riemannian manifold. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
positive second fundamental form, analytic plane domains, chord uniqueness, following continuous observability inequality, bouncing ball orbit, boundary rigidity problem, boundary distance function, isospectral metrics, energy method approach, cutoff operator, insulating cracks, wave invariants, wave trace invariants, ghost orbits, pseudoconvex with respect, sharp trace regularity, outward normal field, unique continuation result, conducting cracks, marked length spectrum, scattering relation, geodesic fibers, strong unique continuation, observability inequalities, real principal symbol Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Pure Appl, Euclidean Laplacian, Siberian Math, Lecture Notes, Annals of Math, Gunther Uhlmann, Springer Verlag, Contemporary Mathematics, Matrix Riccati Comparison Theorem, Applied Mathematics, Inverse Prohl, Michael Vogelius, Marcel Dekker, National Science Foundation, New Geom, Pure Math, Pures Appl, Rio de Janeiro, Springer Lect, University of Virginia New!
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Front Cover | Table of Contents | First Pages | Back Cover | Surprise Me!
Citations (learn more)
This book cites 34
books:
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- Differential Equations (with CD-ROM) by Paul Blanchard on page 175, and page 212
- Science Foundation by Brian Arnold in Front Matter (1), and Front Matter (2)
- Lectures on Partial Differential Equations: Lectures Delivered at the Indian Institute of Science, Bangalore, Under the T.I.F.R.-I.I. Sc. Programme in Applications of Mathematics by G. B. Folland in Back Matter
- Analysis and Optimization of Differential Systems (IFIP Advances in Information and Communication Technology) by Viorel Barbu on page 179
- Stochastic Differential Equations (Siam-Ams Proceedings Ser .: No 6) by N. Y.) Symposium in Applied Mathematics (1972 New York in Front Matter
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