Inverse Problems: Theory and Applications (Contemporary Mathematics)
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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 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.
Size estimates by G. Alessandrini, A. Morassi, and E. Rosset Uniqueness in the inverse conductivity problem for thin imperfections weakly or strongly conducting by V. Bacchelli, C. D. Pagani, and F. Saleri Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of thin inhomogeneities by E. Beretta and E. Francini A resolution study for imaging and time reversal in random media by L. Borcea, G. Papanicolaou, and C. Tsogka Optimal three cylinder inequalities for solutions to parabolic equations with Lipschitz leading coefficients by L. Escauriaza and S. Vessella Some problems for the application of inverse techniques to environmental modeling by M. Giudici Uniqueness and stability in the Cauchy problem for the elasticity system with residual stress by V. Isakov, G. Nakamura, and J.-N. Wang Using a Hankel function expansion to identify stiffness for the boundary impulse input experiment by L. Ji and J. McLaughlin On the uniqueness of solutions of higher order nonlinear dispersive equations by C. E. Kenig, G. Ponce, and L. Vega Reconstruction of a manifold from electromagnetic boundary measurements by Y. V. Kurylev, M. Lassas, and E. Somersalo Direct and inverse problems for second-order integro-differential operator equations in an unbounded time interval by A. Lorenzi and E. Paparoni Geometrical optics for generic anisotropic materials by C. J. Nolan and G. Uhlmann Linear approaches in microwave tomography by M. Piana and M. Bertero Optical tomography in weakly anisotropic scattering media by A. Tamasan Inverse problems in three-body scattering by G. Uhlmann and A. Vasy.
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