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We establish Lipschitz stability for both the potential and the initial conditions from a single boundary measurement in the context of a hyperbolic boundary initial value problem. In our setting, the initial conditions are allowed to…

Analysis of PDEs · Mathematics 2025-11-25 Shiqi Ma

In this paper we address the uniqueness issue in the classical Robin inverse problem on a Lipschitz domain $\Omega\subset\RR^n$, with $L^\infty$ Robin coefficient, $L^2$ Neumann data and isotropic conductivity of class $W^{1,r}(\Omega)$,…

Analysis of PDEs · Mathematics 2016-02-12 Laurent Baratchart , Laurent Bourgeois , Juliette Leblond

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

The problems we address in this paper are the spectral theory and the inverse problems associated with Laplacians on non-compact Riemannian manifolds and more general manifolds admitting conic singularities. In particular, we study the…

Analysis of PDEs · Mathematics 2020-04-15 Hiroshi Isozaki , Matti Lassas

We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field…

Analysis of PDEs · Mathematics 2019-07-05 Yavar Kian , Zhiyuan Li , Yikan Liu , Masahiro Yamamoto

We consider the inverse problem of determining the time independent scalar potential of the dynamic Schr\"odinger equation in an infinite cylindrical domain, from one Neumann boundary observation of the solution. Assuming that this…

Analysis of PDEs · Mathematics 2015-06-15 Yavar Kian , Quang Sang Phan , Eric Soccorsi

We consider a fixed angle inverse scattering problem in the presence of a known Riemannian metric. First, assuming a no caustics condition, we study the direct problem by utilizing the progressing wave expansion. Under a symmetry assumption…

Analysis of PDEs · Mathematics 2021-07-21 Shiqi Ma , Mikko Salo

We present a general framework to study uniqueness, stability and reconstruction for infinite-dimensional inverse problems when only a finite-dimensional approximation of the measurements is available. For a large class of inverse problems…

Analysis of PDEs · Mathematics 2021-11-10 Giovanni S. Alberti , Matteo Santacesaria

We propose a boundary integral formulation for the dynamic problem of electromagnetic scattering and transmission by homogeneous dielectric obstacles. In the spirit of Costabel and Stephan, we use the transmission conditions to reduce the…

Numerical Analysis · Mathematics 2025-05-20 Tonatiuh Sánchez-Vizuet

This paper studies an inverse boundary value problem for a semilinear Helmholtz equation with Neumann boundary conditions in a bounded domain $\Omega \subset \mathbb{R}^n$ ($n\ge2$). The objective is to recover the unknown linear and…

Numerical Analysis · Mathematics 2026-03-10 Long-Ling Du , Zejun Sun , Li-Li Wang , Guang-Hui Zheng

In this paper, we consider inverse scattering and inverse boundary value problems at sufficiently large and fixed energy for the multidimensional relativistic Newton equation with an external potential $V$, $V\in C^2$. Using known results,…

Mathematical Physics · Physics 2009-11-11 Alexandre Jollivet

The paper considers direct and inverse elastic scattering from a cavity in homogeneous medium with Dirichlet and Neumann boundary conditions. For direct scattering, existence and uniqueness are derived by variation approach. For inverse…

Analysis of PDEs · Mathematics 2023-02-28 Tianjiao Wang , Yiwen Lin , Xiang Xu

This paper is concerned with uniqueness in inverse electromagnetic scattering with phaseless far-field pattern at a fixed frequency. In our previous work [{\em SIAM J. Appl. Math.} {\bf 78} (2018), 3024-3039], by adding a known reference…

Analysis of PDEs · Mathematics 2019-06-21 Xiaoxu Xu , Bo Zhang , Haiwen Zhang

This paper gives a remark on the Enclosure Method by considering inverse obstacle scattering problems with a single incident wave whose governing equation is given by the Helmholtz equation in two dimensions. It is concerned with the…

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

Consider time-harmonic acoustic scattering from a bounded penetrable obstacle $D\subset \mathbb R^N$ embedded in a homogeneous background medium. The index of refraction characterizing the material inside $D$ is supposed to be H\"older…

Analysis of PDEs · Mathematics 2015-07-29 Guanghui Hu , Mikko Salo , Esa V. Vesalainen

The acoustic inverse obstacle scattering problem consists of determining the shape of a domain from measurements of the scattered far field due to some set of incident fields (probes). For a penetrable object with known sound speed, this…

Numerical Analysis · Mathematics 2023-02-15 Carlos Borges , Manas Rachh , Leslie Greengard

In this paper we consider the inverse boundary value problem for the Schr\"odinger equation with potential in $L^p$ class, $p>4/3$. We show that the potential is uniquely determined by the boundary measurements.

Analysis of PDEs · Mathematics 2017-04-24 Eemeli Blåsten , Leo Tzou , Jenn-Nan Wang

We study the inverse problem of determining a Signorini obstacle from boundary measurements for the isotropic elasticity system. We prove that the obstacle can be uniquely determined by a single measurement of displacement and normal stress…

Analysis of PDEs · Mathematics 2025-03-26 Maarten V. de Hoop , Matti Lassas , Jinpeng Lu , Lauri Oksanen , Ziyao Zhao

We establish existence and uniqueness results for nonlinear elliptic Dirichlet boundary value problems on n-dimensional time scale domains. Time scales provide a unified framework that encompasses continuous, discrete, and hybrid settings.…

Analysis of PDEs · Mathematics 2026-02-12 Shalmali Bandyopadhyay , F. Ayça Çetinkaya , Tom Cuchta

This paper addresses several geometric inverse problems for some linear parabolic systems where the initial data (and sometimes also the coefficients of the equations) are unknown. The goal is to identify a subdomain within a…

Analysis of PDEs · Mathematics 2025-09-17 Jone Apraiz , Anna Doubova , Enrique Fernández-Cara , Masahiro Yamamoto
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