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Product Code:  CONM/333 
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Electronic ISBN:  9780821879238 
Product Code:  CONM/333.E 
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Book DetailsContemporary MathematicsVolume: 333; 2003; 215 ppMSC: Primary 35; 15; 81; 86; 58;
This volume presents the proceedings of a workshop on Inverse Problems and Applications and a special session on Inverse Boundary Problems and Applications.
Inverse problems arise in practical situations, such as medical imaging, exploration geophysics, and nondestructive evaluation where measurements made in the exterior of a body are used to deduce properties of the hidden interior. A large class of inverse problems arise from a physical situation modeled by partial differential equations. The inverse problem is to determine some coefficients of the equation given some information about solutions. Analysis of such problems is a fertile area for interaction between pure and applied mathematics. This interplay is well represented in this volume where several theoretical and applied aspects of inverse problems are considered.
The book includes articles on a broad range of inverse problems including the inverse conductivity problem, inverse problems for Maxwell's equations, time reversal mirrors, ultrasound using elastic pressure waves, inverse problems arising in the environment, inverse scattering for the threebody problem, and optical tomography. Also included are several articles on unique continuation and on the study of propagation of singularities for hyperbolic equations in anisotropic media.
This volume is suitable for graduate students and research mathematicians interested in inverse problems and applications.ReadershipGraduate students and research mathematicians interested in inverse problems and applications.

Table of Contents

Articles

Giovanni Alessandrini, Antonino Morassi and Edi Rosset  Size estimates [ MR 2032004 ]

V. Bacchelli, C. D. Pagani and F. Saleri  Uniqueness in the inverse conductivity problem for thin imperfections weakly or strongly conducting [ MR 2032005 ]

Elena Beretta and Elisa Francini  Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of thin inhomogeneities [ MR 2032006 ]

Liliana Borcea, George Papanicolaou and Chrysoula Tsogka  A resolution study for imaging and time reversal in random media [ MR 2032007 ]

Luis Escauriaza and Sergio Vessella  Optimal three cylinder inequalities for solutions to parabolic equations with Lipschitz leading coefficients [ MR 2032008 ]

Mauro Giudici  Some problems for the application of inverse techniques to environmental modeling [ MR 2032009 ]

Victor Isakov, Gen Nakamura and JennNan Wang  Uniqueness and stability in the Cauchy problem for the elasticity system with residual stress [ MR 2032010 ]

Lin Ji and Joyce McLaughlin  Using a Hankel function expansion to identify stiffness for the boundary impulse input experiment [ MR 2032011 ]

Carlos E. Kenig, Gustavo Ponce and Luis Vega  On the uniqueness of solutions of higher order nonlinear dispersive equations [ MR 2032012 ]

Yaroslav V. Kurylev, Matti Lassas and Erkki Somersalo  Reconstruction of a manifold from electromagnetic boundary measurements [ MR 2032013 ]

Alfredo Lorenzi and Eva Paparoni  Direct and inverse problems for secondorder integrodifferential operator equations in an unbounded time interval [ MR 2032014 ]

Clifford J. Nolan and Gunther Uhlmann  Geometrical optics for generic anisotropic materials [ MR 2032015 ]

M. Piana and M. Bertero  Linear approaches in microwave tomography [ MR 2032016 ]

Alexandru Tamasan  Optical tomography in weakly anisotropic scattering media [ MR 2032017 ]

Gunther Uhlmann and András Vasy  Inverse problems in threebody scattering [ MR 2032018 ]


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This volume presents the proceedings of a workshop on Inverse Problems and Applications and a special session on Inverse Boundary Problems and Applications.
Inverse problems arise in practical situations, such as medical imaging, exploration geophysics, and nondestructive evaluation where measurements made in the exterior of a body are used to deduce properties of the hidden interior. A large class of inverse problems arise from a physical situation modeled by partial differential equations. The inverse problem is to determine some coefficients of the equation given some information about solutions. Analysis of such problems is a fertile area for interaction between pure and applied mathematics. This interplay is well represented in this volume where several theoretical and applied aspects of inverse problems are considered.
The book includes articles on a broad range of inverse problems including the inverse conductivity problem, inverse problems for Maxwell's equations, time reversal mirrors, ultrasound using elastic pressure waves, inverse problems arising in the environment, inverse scattering for the threebody problem, and optical tomography. Also included are several articles on unique continuation and on the study of propagation of singularities for hyperbolic equations in anisotropic media.
This volume is suitable for graduate students and research mathematicians interested in inverse problems and applications.
Graduate students and research mathematicians interested in inverse problems and applications.

Articles

Giovanni Alessandrini, Antonino Morassi and Edi Rosset  Size estimates [ MR 2032004 ]

V. Bacchelli, C. D. Pagani and F. Saleri  Uniqueness in the inverse conductivity problem for thin imperfections weakly or strongly conducting [ MR 2032005 ]

Elena Beretta and Elisa Francini  Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of thin inhomogeneities [ MR 2032006 ]

Liliana Borcea, George Papanicolaou and Chrysoula Tsogka  A resolution study for imaging and time reversal in random media [ MR 2032007 ]

Luis Escauriaza and Sergio Vessella  Optimal three cylinder inequalities for solutions to parabolic equations with Lipschitz leading coefficients [ MR 2032008 ]

Mauro Giudici  Some problems for the application of inverse techniques to environmental modeling [ MR 2032009 ]

Victor Isakov, Gen Nakamura and JennNan Wang  Uniqueness and stability in the Cauchy problem for the elasticity system with residual stress [ MR 2032010 ]

Lin Ji and Joyce McLaughlin  Using a Hankel function expansion to identify stiffness for the boundary impulse input experiment [ MR 2032011 ]

Carlos E. Kenig, Gustavo Ponce and Luis Vega  On the uniqueness of solutions of higher order nonlinear dispersive equations [ MR 2032012 ]

Yaroslav V. Kurylev, Matti Lassas and Erkki Somersalo  Reconstruction of a manifold from electromagnetic boundary measurements [ MR 2032013 ]

Alfredo Lorenzi and Eva Paparoni  Direct and inverse problems for secondorder integrodifferential operator equations in an unbounded time interval [ MR 2032014 ]

Clifford J. Nolan and Gunther Uhlmann  Geometrical optics for generic anisotropic materials [ MR 2032015 ]

M. Piana and M. Bertero  Linear approaches in microwave tomography [ MR 2032016 ]

Alexandru Tamasan  Optical tomography in weakly anisotropic scattering media [ MR 2032017 ]

Gunther Uhlmann and András Vasy  Inverse problems in threebody scattering [ MR 2032018 ]