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This paper is concerned with the inverse scattering problem of time-harmonic elastic waves by an unbounded rigid rough surface. A direct imaging method is developed to reconstruct the unbounded rough surface from the elastic scattered…

Numerical Analysis · Mathematics 2018-04-17 Xiaoli Liu , Bo Zhang , Haiwen Zhang

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…

Numerical Analysis · Mathematics 2025-06-26 Yao Sun , Yan Chang , Yukun Guo

We consider the inverse elastic scattering of incident plane compressional and shear waves from the knowledge of the far field patterns. Specifically, three direct sampling methods for location and shape reconstruction are proposed using…

Numerical Analysis · Mathematics 2018-03-14 Xia Ji , Xiaodong Liu , Yingxia Xi

In this paper, we consider the direct and inverse problem for isotropic scatterers with two conductive boundary conditions. First, we show the uniqueness for recovering the coefficients from the known far-field data at a fixed incident…

Mathematical Physics · Physics 2024-02-13 Rafael Ceja Ayala , Isaac Harris , Andreas Kleefeld

Monitoring the integrity of elastic structures using ultrasonic waves requires the efficient identification of material parameters from measured surface displacements. The displacement field is governed by Cauchy's equation of motion, i.e.,…

Numerical Analysis · Mathematics 2026-05-20 Benedikt Klein , Mario Ohlberger , Thomas Schuster

The problem of imaging of a moving target is formulated as a Coefficient Inverse Problem for a hyperbolic equation with its coefficient depending on all three spatial variables and time. As the initial condition, the point source running…

Numerical Analysis · Mathematics 2025-12-23 Michael V. Klibanov , Jingzhi Li , Vladimir G. Romanov , Zhipeng Yang

We introduce in this document a direct method allowing to solve numerically inverse type problems for linear parabolic equations. We consider the reconstruction of the full solution of the parabolic equation posed in $\Omega\times (0,T)$ -…

Optimization and Control · Mathematics 2024-02-11 Arnaud Munch , Diego Souza

In this paper, we consider the inverse problem of determining some coefficients within a coupled nonlinear parabolic system, through boundary observation of its non-negative solutions. In the physical setup, the non-negative solutions…

Analysis of PDEs · Mathematics 2024-04-23 Hongyu Liu , Catharine W. K. Lo

The inverse acoustic scattering problems using multi-frequency backscattering far field patterns at isolated directions are studied. The underlying object could be point like scatterers, small scatterers, extended inhomogeneities and…

Analysis of PDEs · Mathematics 2019-10-18 Xia Ji , Xiaodong Liu

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

This paper is concerned with the weak solvability of fully nonlinear parabolic variational inequalities with time dependent convex constraints. As possible approaches to such problems, there are for instance the time-discretization method…

Functional Analysis · Mathematics 2017-06-21 Maria Gokieli , Nobuyuki Kenmochi , Marek Niezgódka

In this paper, we consider the inverse problem of recovering a sound soft scatterer from the measured scattered field. The scattered field is assumed to be induced by a point source on a curve/surface that is known. Here we will propose and…

Analysis of PDEs · Mathematics 2021-10-22 Isaac Harris

It is proposed to monitor spatial and temporal spreads of epidemics via solution of a Coefficient Inverse Problem for a system of three coupled nonlinear parabolic equations. To solve this problem numerically, a version of the so-called…

Numerical Analysis · Mathematics 2025-04-08 Michael V. Klibanov , Trung Truong

This work is concerned with a direct sampling method (DSM) for inverse acoustic scattering problems using far-field data. The method characterizes some unknown obstacles, inhomogeneous media or cracks, directly through an indicator function…

Mathematical Physics · Physics 2012-12-27 Jingzhi Li , Jun Zou

In this paper, we consider the inverse shape problem of recovering isotropic scatterers with a conductive boundary condition. Here, we assume that the measured far-field data is known at a fixed wave number. Motivated by recent work, we…

Analysis of PDEs · Mathematics 2023-05-25 Rafael Ceja Ayala , Isaac Harris , Andreas Kleefeld

We propose a new numerical method for the solution of the problem of the reconstruction of the initial condition of a quasilinear parabolic equation from the measurements of both Dirichlet and Neumann data on the boundary of a bounded…

Analysis of PDEs · Mathematics 2020-09-29 Thuy T. Le , Loc H. Nguyen

We propose a deterministic-statistical method for an inverse source problem using multiple frequency limited aperture far field data. The direct sampling method is used to obtain a disc such that it contains the compact support of the…

Numerical Analysis · Mathematics 2022-09-20 Yanfang Liu , Zhizhang Wu , Jiguang Sun , Zhiwen Zhang

This paper investigates an inverse source problem for general semilinear stochastic hyperbolic equations. Motivated by the challenges arising from both randomness and nonlinearity, we develop a globally convergent iterative regularization…

Analysis of PDEs · Mathematics 2025-04-25 Qi Lü , Yu Wang

Solving parabolic optimal control problems can be inherently challenging in the field of science and engineering, especially with constraints on the nonsmooth distributed control. Motivated by the extensive applicability of the alternating…

Optimization and Control · Mathematics 2026-03-03 Haiming Song , Jinda Yang , Yuran Yang , Jianhua Yuan

This paper is concerned with the electromagnetic inverse scattering problem that aims to determine the location and shape of anisotropic scatterers from far field data (at a fixed frequency). We study the orthogonality sampling method which…

Analysis of PDEs · Mathematics 2019-11-05 Isaac Harris , Dinh-Liem Nguyen