**Contemporary Mathematics**

Volume: 333;
2003;
215 pp;
Softcover

MSC: Primary 35; 15; 81; 86; 58;

Print ISBN: 978-0-8218-3367-4

Product Code: CONM/333

List Price: $69.00

Individual Member Price: $55.20

**Electronic ISBN: 978-0-8218-7923-8
Product Code: CONM/333.E**

List Price: $69.00

Individual Member Price: $55.20

# Inverse Problems: Theory and Applications

Share this page *Edited by *
*Giovanni Alessandrini; Gunther Uhlmann*

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 non-destructive 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 three-body 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.

#### Table of Contents

# Table of Contents

## Inverse Problems: Theory and Applications

- Contents iii4 free
- Preface v6 free
- Size estimates 18 free
- Uniqueness in the inverse conductivity problem for thin imperfections weakly or strongly conducting 3542
- Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of thin inhomogeneities 4956
- A resolution study for imaging and time reversal in random media 6370
- Optimal three cylinder inequalities for solutions to parabolic equations with Lipschitz leading coefficients 7986
- Some problems for the application of inverse techniques to environmental modeling 8996
- Uniqueness and stability in the Cauchy problem for the elasticity system with residual stress 99106
- Using a Hankel function expansion to identify stiffness for the boundary impulse input experiment 115122
- On the uniqueness of solutions of higher order nonlinear dispersive equations 137146
- Reconstruction of a manifold from electromagnetic boundary measurements 147156
- Direct and inverse problems for second-order integro-differential operator equations in an unbounded time interval 163172
- Geometrical optics for generic anisotropic materials 177186
- Linear approaches in microwave tomography 187196
- Optical tomography in weakly anisotropic scattering media 199208
- Inverse problems in three-body scattering 209218

#### Readership

Graduate students and research mathematicians interested in inverse problems and applications.