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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…
We consider the inverse boundary value problem for the system of equations describing elastic waves in isotropic media on a bounded domain in $\mathbb{R}^3$ via a finite-time Laplace transform. The data is the dynamical Dirichlet-to-Neumann…
In this study, we address the inverse problem of recovering the Lam\'e parameters ($\lambda, \mu$) and the density $\rho$ of a medium from the Neumann-to-Dirichlet map for any dimension $d\geq 2$. This inverse problem finds its motivation…
This paper studies pressure-robustness for the axisymmetric Stokes problem. The transformation to cylindrical coordinates requires that the radially weighted velocity is divergence-free in the classical sense. Consequently, traditional…
This paper proposes direct and inverse results for the Dirichlet and Dirichlet to Neumann problems for complex curves with nodal type singularities. As an application, we give a method to reconstruct the conformal structure of a compact…
We consider an inverse problem for the Boltzmann equation with nonlinear collision operator in dimensions $n\geq 2$. We show that the kinetic collision kernel can be uniquely determined from the incoming-to-outgoing mappings on the boundary…
We consider an inverse problem of recovering the non-linearity in the one dimensional variable exponent $p(x)$-Laplace equation from the Dirichlet-to-Neumann map. The variable exponent can be recovered up to the natural obstruction of…
We study the factorization and monotonicity method for inverse acoustic scattering problems. Firstly, we give a new general functional analysis theorem for the monotonicity method. Comparing with the factorization method, the general…
The aim of this paper is to establish a nonlinear variational approach to the reconstruction of moving density images from indirect dynamic measurements. Our approach is to model the dynamics as a hyperelastic deformation of an initial…
We consider the inverse problem of reconstructing inhomogeneities by performing a finite number of scattering measurements of acoustic type in the time-harmonic setting. We set up the reconstruction as a fully discrete variational problem…
Elasticity image, visualizing the quantitative map of tissue stiffness, can be reconstructed by solving an inverse problem. Classical methods for magnetic resonance elastography (MRE) try to solve a regularized optimization problem…
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…
In this article we deal with a class of geometric inverse problem for bottom detection by one single measurement on the free surface in water--waves. We found upper and lower bounds for the size of the region enclosed between two different…
An exact transformation method is introduced that reduces the governing equations of a continuum structure coupled to strong nonlinearities to a low dimensional equation with memory. The method is general and well suited to problems with…
In this paper, we will discuss the use of a Sampling Method to reconstruct impenetrable inclusions from Electrostatic Cauchy data. We consider the case of a perfectly conducting and impedance inclusion. In either case, we show that the…
The inverse scattering problem for biharmonic waves, governing flexural vibrations of elastic plates, presents fundamental analytical challenges distinct from acoustic inverse problems due to the fourth-order differential operator and…
We consider an inverse problem for the elastic wave of simultaneously reconstructing the impedance and the geometric information of the bounded body that is occupied by a homogeneous and isotropic elastic medium from the measured Cauchy…
The recovery of the intrinsic geometric structures of data collections is an important problem in data analysis. Supervised extensions of several manifold learning approaches have been proposed in the recent years. Meanwhile, existing…
We develop a linearized boundary control method for the inverse boundary value problem of determining the damping coefficient in the damped wave equation. The objective is to reconstruct an unknown perturbation in a known background damping…
We develop a linearized boundary control method for the inverse boundary value problem of determining a density in the acoustic wave equation. The objective is to reconstruct an unknown perturbation in a known background density from the…