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Partial Differential Equations and Inverse Problems
Edited by: Carlos Conca, Raúl Manásevich, Gunther Uhlmann, and Michael S. Vogelius
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Contemporary Mathematics
2004; 410 pp; softcover
Volume: 362
ISBN-10: 0-8218-3448-7
ISBN-13: 978-0-8218-3448-0
List Price: US$109
Member Price: US$87.20
Order Code: CONM/362
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This collection of articles from the Proceedings of the Pan-American Advanced Studies Institute reflects recent developments in partial differential equations, nonlinear analysis and inverse problems.

Interactions among these topics have produced remarkable developments over the last couple of decades. This volume contains survey articles reflecting the work of leading experts who presented minicourses at the event. Contributors include J. Busca, Y. Capdeboscq, M.S. Vogelius, F. A. Grünbaum, L. F. Matusevich, M. de Hoop, and P. Kuchment.

The volume is suitable for graduate students and researchers interested in partial differential equations and their applications in nonlinear analysis and inverse problems.

Readership

Graduate students and research mathematicians interested in partial differential equations and their applications in nonlinear analysis and inverse problems.

Table of Contents

  • T. Aktosun -- Inverse scattering on the line with incomplete scattering data
  • M. S. Ashbaugh -- On universal inequalities for the low eigenvalues of the buckling problem
  • J. Baras, C. Berenstein, and F. Gavilánez -- Continuous and discrete inverse conductivity problems
  • R. D. Benguria and M. Loss -- Connection between the Lieb-Thirring conjecture for Schrödinger operators and an isoperimetric problem for ovals on the plane
  • J. Busca -- An introduction to PDE methods in finance
  • Y. Capdeboscq and M. S. Vogelius -- A review of some recent work on impedance imaging for inhomogeneities of low volume fraction
  • F. A. C. C. Chalub and J. P. Zubelli -- Matrix bispectrality and Huygens' principle for Dirac operators
  • A. J. Corcho and F. Linares -- Well-posedness for the Schrödinger-Debye equation
  • A. Dall'Acqua and G. Sweers -- On domains for which the clamped plate system is positivity preserving
  • M. Di Francesco and P. A. Markowich -- Entropy dissipation and Wasserstein metric methods for the viscous Burgers' equation: convergence to diffusive waves
  • J. Dolbeault, D. Kinderlehrer, and M. Kowalczyk -- Remarks about the flashing rachet
  • N. Ghoussoub and R. J. McCann -- A least action principle for steepest descent in a non-convex landscape
  • F. A. Grünbaum and L. F. Matusevich -- A network tomography problem related to the hypercube
  • A. Hassell and J. Wunsch -- On the structure of the Schrödinger propagator
  • M. V. de Hoop -- The downward continuation approach to modeling and inverse scattering of seismic data in the Kirchhoff approximation
  • M. Kowalczyk -- Approximate invariant manifold of the Allen-Cahn flow in two dimensions
  • P. Kuchment -- On some spectral problems of mathematical physics
  • M. Lassas, L. Päivärinta, and E. Saksman -- Inverse problem for a random potential
  • R. Mazzeo -- Pseudodifferential analysis for the Laplacian on noncompact symmetric spaces
  • G. A. Mendoza -- Boundary structure and cohomology of \(b\)-complex manifolds
  • G. Nakamura, G. Uhlmann, and J.-N. Wang -- Unique continuation property for elliptic systems and crack determination in anisotropic elasticity
  • M. del Pino, J. Dolbeault, and M. Musso -- Duality in sub-supercritical bubbling in the Brezis-Nirenberg problem near the critical exponent
  • F. Reitich -- High-order domain variations in boundary value and free boundary problems
  • A. S. Barreto -- Radiation fields and inverse scattering on asymptotically Euclidean manifolds
  • C. Timofte and C. Conca -- Interactive oscillation sources in Signorini's type problems
  • R. Weder -- Inverse scattering with time-periodic potentials
  • R. Weikard -- A local Borg-Marchenko theorem for difference equations with complex coefficients
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