Analysis of Anisotropic Inverse Boundary Value Problems
Lead Research Organisation:
University College London
Department Name: Mathematics
Abstract
Effects of anisotropy are important in electrical, acoustical and optical imaging used in non-destructive testing, geophysics and medical imaging. If ignored these effects can result in a wrong solution to the inverse problem. There are currently very few theoretical results on scalar anisotropic inverse problems with no general approach towards stability and development of convergent reconstruction algorithms for solving these problems. Almost nothing is known about inverse boundary value problems for systems of partial differential equations, especially in the anisotropic case. The aim of this research is to develop analytical and geometric methods to study uniqueness and stability in anisotropic inverse problems and to implement these methods by developing convergent reconstruction algorithms for solving fully non-linear inverse boundary value problems.
Organisations
People |
ORCID iD |
| Yaroslav Kurylev (Principal Investigator) |
Publications
Bosi R
(2016)
Stability of the unique continuation for the wave operator via Tataru inequality and applications
in Journal of Differential Equations
Faraco D
(2014)
G-convergence, Dirichlet to Neumann maps and invisibility
in Journal of Functional Analysis
Greenleaf A
(2018)
Superdimensional Metamaterial Resonators From Sub-Riemannian Geometry
in SIAM Journal on Applied Mathematics
Greenleaf A
(2009)
Cloaking Devices, Electromagnetic Wormholes, and Transformation Optics
in SIAM Review
Greenleaf A
(2011)
Approximate Quantum and Acoustic Cloaking
in Journal of Spectral Theory
Greenleaf A
(2012)
Cloaked electromagnetic, acoustic, and quantum amplifiers via transformation optics.
in Proceedings of the National Academy of Sciences of the United States of America
Greenleaf A
(2011)
Cloaking a sensor via transformation optics.
in Physical review. E, Statistical, nonlinear, and soft matter physics
Isozaki H
(2017)
Conic singularities, generalized scattering matrix, and inverse scattering on asymptotically hyperbolic surfaces
in Journal für die reine und angewandte Mathematik (Crelles Journal)
| Description | 1. Some geometric-based conditions which yield stability in inverse problems are found. 2. New directions in the mathematical theory of invisibility/cloaking are obtained |
| Exploitation Route | Blueprints for devices based transformation optics may be, in the long run, be used in some engineering and medical applications |
| Sectors | Healthcare,Manufacturing, including Industrial Biotechology,Other |
| Description | A number of researchers in material sciences used our results on invisibility and related topics, in particular, wormholes and approximation by isotropic materials. |
| First Year Of Impact | 2013 |
| Sector | Manufacturing, including Industrial Biotechology,Other |
| Impact Types | Economic |