相关论文: On an inverse problem for the plate equation with …

We propose bending energies for isotropic elastic plates and shells. For a plate, we define and employ a surface tensor that symmetrically couples stretch and curvature such that any elastic energy density constructed from its invariants is…

We consider the problem of determining the unknown boundary values of a solution of an elliptic equation outside a bounded open set $B$ from the knowledge of the values of this solution on a boundary of an arbitrary Lipschitz bounded domain…

We consider the inverse problem of estimating the shape profile of an unknown deposit from a set of eddy current impedance measurements. The measurements are acquired with an axial probe, which is modeled by a set of coils that generate a…

In this work, we study the problem of reconstructing shapes from simple nonasymptotic densities measured only along shape boundaries. The particular density we study is also known as the integral area invariant and corresponds to the area…

We consider the problem of identifying possibly discontinuous doping profiles in semiconductor devices from data obtained by\,stationary voltage-current maps. In particular, we focus on the so-called unipolar case, a system of PDE's derived…

This paper is concerned with the inverse moving source problems for parabolic equations. Given the temporal function, we prove the uniqueness of the nonlinear inverse problem of determining the orbit function by final data measured in a…

The tilted-wave interferometer is a promising technique for the development of a reference measurement system for the highly accurate form measurement of aspheres and freeform surfaces. The technique combines interferometric measurements,…

Inverse problem to determine simultaneously a general space- and time-dependent source and an initial state in a fractional diffusion equation from an {\it a posteriori} measurement of the normal derivative of the state on a portion of a…

This paper is concerned with an inverse wavenumber/frequency-dependent source problem for the Helmholtz equation. In two and three dimensions, the unknown source term is supposed to be compactly supported in spatial variables but…

A method to retrieve the elastic constants of rectangular wooden plates is presented, relying on the measurement of a set of eigenfrequencies and the identification of the corresponding mode shapes, and belonging to the more general…

A comprehensive convergence and stability analysis of some probabilistic numerical methods designed to solve Cauchy-type inverse problems is performed in this study. Such inverse problems aim at solving an elliptic partial differential…

Recent developments in imaging techniques and correlation algorithms enable measurement of strain fields on a deforming material at high spatial and temporal resolution. In such cases, the computation of the stress field from the known…

We consider the problem of identifying discontinuous doping profiles in semiconductor devices from data obtained by different models connected to the voltage-current map. Stationary as well as transient settings are discussed and a…

The focus of this book is on the analysis of regularization methods for solving \emph{nonlinear inverse problems}. Specifically, we place a strong emphasis on techniques that incorporate supervised or unsupervised data derived from prior…

We investigate a two-dimensional transmission model consisting of a wave equation and a Kirchhoff plate equation with dynamical boundary controls under geometric conditions. The two equations are coupled through transmission conditions…

This paper investigates the geometric inverse problem of recovering the bottom shape from surface measurements of water waves. Using the general water-waves system on a bounded subdomain of the fluid domain, we address this inverse problem,…

We study the inverse problem for determining the time-dependent matrix potential appearing in the wave equation. We prove the unique determination of potential from the knowledge of solution measured on a part of the boundary.

In this paper, we study an inverse problem for linear parabolic system with variable diffusion coefficients subject to dynamic boundary conditions. We prove a global Lipschitz stability for the inverse problem involving a simultaneous…

In this paper, we study simultaneous determination of the strain hardening exponent, the shear modulus and the yield stress in an inverse problem. First, we analyze the direct and the inverse problems. Then we formulate the inverse problem…

We consider the inverse source problem of determining a source term depending on both time and space variable for fractional and classical diffusion equations in a cylindrical domain from boundary measurements. With suitable boundary…