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We use Ikehata's enclosure method to reconstruct penetrable unknown inclusions in a plane elastic body in time-harmonic waves. Complex geometrical optics solutions with complex polynomial phases are adopted as the probing utility. In a…

Analysis of PDEs · Mathematics 2011-09-13 Rulin Kuan

We study boundary determination for an inverse problem associated to the time-harmonic Maxwell equations and another associated to the isotropic elasticity system. We identify the electromagnetic parameters and the Lam\'e moduli for these…

Analysis of PDEs · Mathematics 2019-03-11 Pedro Caro , Ru-Yu Lai , Yi-Hsuan Lin , Ting Zhou

We consider the inverse problem of determining the Lam\'{e} parameters and the density of a three-dimensional elastic body from the local time-harmonic Dirichlet-to-Neumann map. We prove uniqueness and Lipschitz stability of this inverse…

Analysis of PDEs · Mathematics 2014-12-12 Elena Beretta , Maarten V. de Hoop , Elisa Francini , Sergio Vessella , Jian Zhai

Detecting inhomogeneities in the electrical conductivity is a special case of the inverse problem in electrical impedance tomography, that leads to fast direct reconstruction methods. One such method can, under reasonable assumptions,…

Numerical Analysis · Mathematics 2018-08-16 Henrik Garde

We generalize recent results on the monotonicity method, for inclusion detection in the partial data anisotropic Calder\'on problem, to very general non-self-adjoint perturbations. This involves a forward model that accounts for both the…

Analysis of PDEs · Mathematics 2026-05-07 Henrik Garde , David Johansson , Thanasis Zacharopoulos

We focus on a geometrical inverse problem that involves recovering discontinuities in electrical conductivity based on boundary measurements. This problem serves as a model to introduce a shape recovery technique that merges the…

Numerical Analysis · Mathematics 2025-01-28 Bastian Harrach , Houcine Meftahi

In electrical impedance tomography, algorithms based on minimizing a linearized residual functional have been widely used due to their flexibility and good performance in practice. However, no rigorous convergence results have been…

Analysis of PDEs · Mathematics 2018-10-11 Bastian Harrach , Mach Nguyet Minh

The inverse problem of electrical impedance tomography is severely ill-posed, meaning that, only limited information about the conductivity can in practice be recovered from boundary measurements of electric current and voltage. Recently it…

Analysis of PDEs · Mathematics 2018-09-20 Henrik Garde , Stratos Staboulis

We investigate an inverse source problem of the time-harmonic elastic wave equation. Some novel sampling-type numerical schemes are proposed to identify the moment tensor point sources in the Lam\'e system from near-field measurements.…

Numerical Analysis · Mathematics 2021-11-24 Xianchao Wang , Yukun Guo , Sara Bousba

We study the inverse boundary value problem for the linear elastic wave equation in three-dimensional isotropic medium. We show that both the Lam\'e parameters and the density can be uniquely recovered from the boundary measurements under…

Analysis of PDEs · Mathematics 2025-12-22 Jian Zhai

The monotonicity-based approach has become one of the fundamental methods for reconstructing inclusions in the inverse problem of electrical impedance tomography. Thus far the method has not been proven to be able to handle extreme…

Analysis of PDEs · Mathematics 2021-02-05 Valentina Candiani , Jérémi Dardé , Henrik Garde , Nuutti Hyvönen

In this paper we establish that the time-harmonic elasticity problem in a half-strip with non-homogeneous Dirichlet conditions on its boundary section and traction-free conditions on its upper and lower boundaries, has a unique weak…

Analysis of PDEs · Mathematics 2022-06-27 Jean-Luc Akian

We propose a novel numerical homogenization method based on the edge multiscale approach for solving indefinite time-harmonic Maxwell equations in heterogeneous media with large wavenumber. Numerical methods for these equations in…

Numerical Analysis · Mathematics 2026-04-27 Yueqi Wang , Wing Tat Leung , Guanglian Li

Here homogenization theory is used to establish a connection between the symmetries of a periodic elastic structure associated with the microscopic properties of an elastic material and the material symmetries of the effective, macroscopic…

Mathematical Physics · Physics 2015-12-29 Mariya Ptashnyk , Brian Seguin

This paper is concerned with homogenization of systems of linear elasticity with rapidly oscillating periodic coefficients. We establish sharp convergence rates in $L^2$ for the mixed boundary value problems with bounded measurable…

Analysis of PDEs · Mathematics 2017-02-14 Zhongwei Shen , Jinping Zhuge

Transient Elastography enables detection and characterization of tissue abnormalities. In this paper we assume that the displacements are modeled by linear isotropic elasticity system and the tissue displacement has been obtained by the…

Analysis of PDEs · Mathematics 2013-08-08 Ru-Yu Lai

Within the framework of linear elasticity we assume the availability of internal full-field measurements of the continuum deformations of a non-homogeneous isotropic solid. The aim is the quantitative reconstruction of the associated…

Analysis of PDEs · Mathematics 2015-06-17 Guillaume Bal , Cédric Bellis , Sébastien Imperiale , François Monard

We consider an inverse problem in elastodynamics arising in seismic imaging. We prove locally uniqueness of the density of a non-homogeneous, isotropic elastic body from measurements taken on a part of the boundary. We measure the Dirichlet…

Analysis of PDEs · Mathematics 2018-10-17 Sombuddha Bhattacharyya

We consider a linearized inverse scattering problem for elastic waves. We prove that a fully anisotropic perturbation of the elastic parameters around an isotropic and homogeneous reference can be uniquely determined by (single-)scattered…

Analysis of PDEs · Mathematics 2026-05-01 Matti Lassas , Shiqi Ma , Lauri Oksanen , Mikko Salo , Jian Zhai

Assuming homogeneous isotropic Lambda-CDM cosmology allows Lambda, spatial curvature and dark matter density to be inferred from large scale structure observations such as supernovae. The purpose of this paper is to extend this to allow…

General Relativity and Quantum Cosmology · Physics 2011-02-02 Toby Wiseman , Benjamin Withers