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This paper is concerned with a new type of inverse obstacle problem governed by a variable-order time-fraction diffusion equation in a bounded domain. The unknown obstacle is a region where the space dependent variable-order of fractional…

Analysis of PDEs · Mathematics 2022-02-18 Masaru Ikehata , Yavar Kian

A version of the so-called "convexification" numerical method for a coefficient inverse scattering problem for the 3D Hemholtz equation is developed analytically and tested numerically. Backscattering data are used, which result from a…

Numerical Analysis · Mathematics 2018-01-16 Michael V. Klibanov , Aleksandr E. Kolesov

We consider the elastic wave scattering problem involving rigid obstacles. This work addresses the inverse problem of reconstructing the position and shape of such obstacles using far-field measurements. A novel monotonicity-based approach…

Analysis of PDEs · Mathematics 2025-06-06 Mengjiao Bai , Huaian Diao , Weisheng Zhou

This paper is concerned with the inverse acoustic scattering problems by an obstacle or a cavity with a sound-soft or a sound-hard boundary. A direct imaging method relying on the boundary conditions is proposed for reconstructing the shape…

Numerical Analysis · Mathematics 2022-02-21 Deyue Zhang , Yue Wu , Yinglin Wang , Yukun Guo

Wave propagation and acoustic scattering problems require vast computational resources to be solved accurately at high frequencies. Asymptotic methods can make this cost potentially frequency independent by explicitly extracting the…

Numerical Analysis · Mathematics 2018-01-16 Daan Huybrechs , Peter Opsomer

An inverse boundary value problem for the Helmholtz equation in a bounded domain is considered. The problem is to extract information about an unknown obstacle embedded in the domain with unknown impedance boundary condition (the Robin…

Analysis of PDEs · Mathematics 2010-02-16 Masaru Ikehata

High frequency estimates for the Dirichlet-to-Neumann and Neumann-to-Dirichlet operators are obtained for the Helmholtz equation in the exterior of bounded obstacles. These a priori estimates are used to study the scattering of plane waves…

Mathematical Physics · Physics 2013-07-18 Evgeny Lakshtanov , Boris Vainberg

We consider the inverse scattering problem to reconstruct a local perturbation of a given inhomogeneous periodic layer in $\mathbb{R}^d$, $d=2,3$, using near field measurements of the scattered wave on an open set of the boundary above the…

Analysis of PDEs · Mathematics 2024-12-20 Alexander Konschin , Armin Lechleiter

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…

Numerical Analysis · Mathematics 2026-05-05 Tielei Zhu , Zhihao Ge , Bangmin Wu

This paper is concerned with analysis of electromagnetic wave scattering by an obstacle which is embedded in a two-layered lossy medium separated by an unbounded rough surface. Given a dipole point source, the direct problem is to determine…

Analysis of PDEs · Mathematics 2019-09-04 Peijun Li , Jue Wang , Lei Zhang

Inverse scattering problems have many important applications. In this paper, given limited aperture data, we propose a Bayesian method for the inverse acoustic scattering to reconstruct the shape of an obstacle. The inverse problem is…

Analysis of PDEs · Mathematics 2019-05-30 Zhaoxiang Li , Zhiliang Deng , Jiguang Sun

We consider the scattering problem governed by the Helmholtz equation with inhomogeneity in both `conductivity' in the divergence form and `potential' in the lower order term. The support of the inhomogeneity is assumed to contain a convex…

Analysis of PDEs · Mathematics 2020-09-14 Fioralba Cakoni , Jingni Xiao

An inverse obstacle scattering problem for the electromagnetic wave governed by the Maxwell system over a finite time interval is considered. It is assumed that the wave satisfies the Leontovich boundary condition on the surface of an…

Analysis of PDEs · Mathematics 2019-02-22 Masaru Ikehata

It is well known that the modulus of the far-field pattern (or phaseless far-field pattern) is invariant under translations of the scattering obstacle if only one plane wave is used as the incident field, so the shape but not the location…

Numerical Analysis · Mathematics 2017-06-07 Bo Zhang , Haiwen Zhang

In this paper, a new model is proposed for the inverse random source scattering problem of the Helmholtz equation with attenuation. The source is assumed to be driven by a fractional Gaussian field whose covariance is represented by a…

Analysis of PDEs · Mathematics 2019-11-27 Peijun Li , Xu Wang

The scattering of quasiperiodic waves for a two-dimensional Helmholtz equation with a constant refractive index perturbed by a function which is periodic in one direction and of finite support in the other is considered. The scattering…

Mathematical Physics · Physics 2019-10-23 P. Zhevandrov , A. Merzon , M. I. Romero Rodríguez , J. E. de la Paz Méndez

This paper is concerned with uniqueness in inverse acoustic scattering with phaseless far-field data at a fixed frequency. The main difficulty of this problem is the so-called translation invariance property of the modulus of the far-field…

Analysis of PDEs · Mathematics 2017-09-26 Xiaoxu Xu , Bo Zhang , Haiwen Zhang

In this paper, we will study increasing stability in the inverse source problem for the Helmholtz equation in the plane when the source term is assumed to be compactly supported in a bounded domain $\Omega$ with sufficiently smooth…

Analysis of PDEs · Mathematics 2018-04-18 Mozhgan Nora Entekhabi , Victor Isakov

This paper is concerned with time domain forward scattering and inverse scattering problems with a single moving point source as the emitter. Approximate solutions are provided for the forward scattering problem with a moving emitter.…

Numerical Analysis · Mathematics 2025-10-13 Yu Sun , Bo Chen , Peng Gao , Qiuyi Li , Yao Sun

The problem of reconstruction of an unknown refractive index $k(x)$ of an inhomogeneous solid $P$ is considered. The refractive index is assumed to be a piecewise-H\"{o}lder function The original boundary value problem for the Helmholtz…

Numerical Analysis · Mathematics 2018-03-14 Mikhail Medvedik , Yury Smirnov , Aleksei Tsupak