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The aim of this paper is to establish the framework of the enclosure method for some class of inverse problems whose governing equations are given by parabolic equations with discontinuous coefficients. The framework is given by considering…

Analysis of PDEs · Mathematics 2011-09-21 Masaru Ikehata

It is well known that the Fourier series Dirichlet-to-Neumann (DtN) boundary condition can be used to solve the Helmholtz equation in unbounded domains. In this work, applying such DtN boundary condition and using the finite element method,…

Numerical Analysis · Mathematics 2019-02-12 Liwei Xu , Tao Yin

Existence and uniqueness of the scattering solutions is proved for a class of bounded rough obstacles which is much larger than the class of Lipschitz obstacles. Integral equations method is not used. The approach is based on the…

Mathematical Physics · Physics 2007-05-23 A. G. Ramm , M. Sammartino

This paper presents a numerical method for the simulation of fluid-structure interaction specifically tailored to interactions between Newtonian fluids and a large number of slender viscoelastic Cosserat rods. Because of their high…

Soft Condensed Matter · Physics 2022-01-13 S. Tschisgale , J. Fröhlich

We introduce and study a new inverse problem for antiplane shear in elastic bodies with strain-gradient interfaces. The setting is a homogeneous isotropic elastic body containing an inclusion separated by a thin interface endowed with…

Analysis of PDEs · Mathematics 2025-09-19 Govanni Granados , Jeremy L. Marzuola , Casey Rodriguez

In this article, we study the inverse scattering problem for the nonlinear fractional Helmholtz equation with cubic nonlinearity in three dimensions, where we recover a compactly supported potential from scattering amplitude.

Analysis of PDEs · Mathematics 2026-03-30 Saumyajit Das , Susovan Pramanik

The inverse quantum scattering problem for the perturbed Bessel equation is considered. A direct and practical method for solving the problem is proposed. It allows one to reduce the inverse problem to a system of linear algebraic…

Mathematical Physics · Physics 2020-12-30 Vladislav V. Kravchenko , Elina L. Shishkina , Sergii M. Torba

The hodograph of the Kepler-Coulomb problem, that is, the path traced by its velocity vector, is shown to be a circle and then it is used to investigate other properties of the motion. We obtain the configuration space orbits of the problem…

We establish H\"older stability of an inverse hyperbolic obstacle problem. Mainly, we study the problem of reconstructing an unknown function defined on the boundary of the obstacle from two measurements taken on the boundary of a domain…

Analysis of PDEs · Mathematics 2025-03-24 Mourad Choulli , Hiroshi Takase

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

We develop a shape-Newton method for solving generic free-boundary problems where one of the free-boundary conditions is governed by the Bernoulli equation. The Newton-like scheme is developed by employing shape derivatives in the weak…

Numerical Analysis · Mathematics 2024-09-24 Yiyun Fan , John Billingham , Kristoffer van der Zee

This paper is concerned with the inverse medium problem of determining the location and shape of penetrable scattering objects from measurements of the scattered field. We study a sampling indicator function for recovering the scattering…

Numerical Analysis · Mathematics 2023-03-13 Dinh-Liem Nguyen , Trung Truong

The paper is concerned with the three-dimensional electromagnetic scattering from a large open rectangular cavity that is embedded in a perfectly electrically conducting infinite ground plane. By introducing a transparent boundary…

Numerical Analysis · Mathematics 2021-04-28 Yanli Chen , Xue Jiang , Jun Lai , Peijun Li

In this paper we review some recent results concerning inverse problems for thin elastic plates. The plate is assumed to be made by non-homogeneous linearly elastic material belonging to a general class of anisotropy. A first group of…

Analysis of PDEs · Mathematics 2012-09-28 Antonino Morassi , Edi Rosset , Sergio Vessella

Due to manufacturing defects or wear and tear, industrial components may have uncertainties. In order to evaluate the performance of machined components, it is crucial to quantify the uncertainty of the scattering surface. This brings up an…

Numerical Analysis · Mathematics 2025-04-28 Yi Wang , Lei Lin , Junliang Lv

We study the validity of the Neumann or Born series approach in solving the Helmholtz equation and coefficient identification in related inverse scattering problems. Precisely, we derive a sufficient and necessary condition under which the…

Numerical Analysis · Mathematics 2023-07-18 Mirza Karamehmedović , Faouzi Triki

In this paper, we consider two time-harmonic inverse scattering problems of reconstructing penetrable inhomogeneous obstacles from near field measurements. First we appeal to the Born approximation for reconstructing small isotropic…

Analysis of PDEs · Mathematics 2017-01-18 Isaac Harris , Scott Rome

In this paper we the formulation of inverse problems as constrained minimization problems and their iterative solution by gradient or Newton type. We carry out a convergence analysis in the sense of regularization methods and discuss…

Numerical Analysis · Mathematics 2021-01-15 Barbara Kaltenbacher , Kha Van Huynh

An inverse problem for the wave equation outside an obstacle with a {\it dissipative boundary condition} is considered. The observed data are given by a single solution of the wave equation generated by an initial data supported on an open…

Analysis of PDEs · Mathematics 2016-07-22 Masaru Ikehata

Consider the problem of inverse scattering of time-harmonic point sources from an infinite, penetrable rough interface with bounded obstacles buried in the lower half-space, where the interface is assumed to be a local perturbation of a…

Analysis of PDEs · Mathematics 2020-09-02 Jianliang Li , Jiaqing Yang , Bo Zhang