English
Related papers

Related papers: Two sides of probe method and obstacle with impeda…

200 papers

This paper considers to the problems of diffraction of electromagnetic waves on a half-plane, which has a finite inclusion in the form of a Lipschitz curve. The diffraction problem formulated as boundary value problem for Helmholtz…

Mathematical Physics · Physics 2018-03-06 E. Lipachev

In this paper, we study the inverse problem for determining an unknown time-dependent source coefficient in a semilinear pseudo-parabolic equation with variable coefficients and Neumann boundary condition. This unknown source term is…

Analysis of PDEs · Mathematics 2025-11-20 K. Van Bockstal , K. Khompysh

We investigate an inverse Robin spectral problem for the $p$-Laplace operator on a bounded domain with mixed Dirichlet-Robin boundary conditions. The aim is to identify an unknown Robin coefficient on an inaccessible boundary portion from…

Analysis of PDEs · Mathematics 2026-03-10 Farid Bozorgnia , Olimjon Eshkobilov

We consider a transmission problem for the Helmholtz equation across the boundary of an extension domain. A such boundary can be Lipschitz, fractal, or of varying Hausdorff dimension for instance. We generalise the notions of layer…

Analysis of PDEs · Mathematics 2026-01-22 Gabriel Claret

We relax the regularity condition on potentials of Schr\"odinger equations in the uniqueness results in \cite{EB} and \cite{IY2} for the inverse boundary value problem of determining a potential by Dirichlet-to-Neumann map.

Mathematical Physics · Physics 2012-08-21 Oleg Yu. Imanuvilov , Masahiro Yamamoto

We consider a restricted Dirichlet-to-Neumann map associated to a wave type operator on a Riemannian manifold with boundary. The restriction corresponds to the case where the Dirichlet traces are supported on one subset of the boundary and…

Analysis of PDEs · Mathematics 2018-06-15 Yavar Kian , Yaroslav Kurylev , Matti Lassas , Lauri Oksanen

This paper gives a note on an application of the enclosure method to an inverse obstacle scattering problem governed by the Helmholtz equation in two dimensions. It is shown that one can uniquely determine the convex hull of an unknown…

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

We consider the inverse problem of determining coefficients appearing in semilinear elliptic equations stated on Riemannian manifolds with boundary given the knowledge of the associated Dirichlet-to-Neumann map. We begin with a negative…

Analysis of PDEs · Mathematics 2024-06-18 Ali Feizmohammadi , Yavar Kian , Lauri Oksanen

We consider approximating the solution of the Helmholtz exterior Dirichlet problem for a nontrapping obstacle, with boundary data coming from plane-wave incidence, by the solution of the corresponding boundary value problem where the…

Numerical Analysis · Mathematics 2023-06-23 Jeffrey Galkowski , David Lafontaine , Euan A. Spence

An inverse problem of finding an obstacle and the boundary condition on its surface from the fixed-energy scattering data is studied. A new method is developed for a proof of the uniqueness results. The method does not use the discreteness…

Mathematical Physics · Physics 2007-05-23 A. G. Ramm

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…

Analysis of PDEs · Mathematics 2025-03-14 Mourad Choulli , Hiroshi Takase

We consider Calder\'{o}n's inverse boundary value problems for a class of nonlinear Helmholtz Schr\"{o}dinger equations and Maxwell's equations in a bounded domain in $\R^n$. The main method is the higher-order linearization of the…

Analysis of PDEs · Mathematics 2022-07-01 Xuezhu Lu

A non-conventional shape optimization approach is introduced to address the identification of an obstacle immersed in a fluid described by the Stokes equation within a larger bounded domain, relying on boundary measurements on the…

Optimization and Control · Mathematics 2024-03-19 Julius Fergy Tiongson Rabago , Lekbir Afraites , Hirofumi Notsu

Boundary value problems for second-order elliptic equations in divergence form, whose nonlinearity is governed by a convex function of non-necessarily power type, are considered. The global boundedness of their solutions is established…

Analysis of PDEs · Mathematics 2022-07-18 Giuseppina Barletta , Andrea Cianchi , Greta Marino

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

In this paper, we consider the inverse boundary value problem of the elliptic operator $\Delta+q$ in a fixed region $\Omega\subset\mathbb{R}^3$ with unknown embedded obstacles $D$. In particular, we give a new and simple proof to uniquely…

Analysis of PDEs · Mathematics 2025-03-04 Chengyu Wu , Jiaqing Yang

In this paper we study the inverse boundary value problem of determining the potential in the Schr\"{o}dinger equation from the knowledge of the Dirichlet-to-Neumann map, which is commonly accepted as an ill-posed problem in the sense that,…

Analysis of PDEs · Mathematics 2012-11-29 Elena Beretta , Maarten V. de Hoop , Lingyun Qiu

In the present paper, we consider a non self adjoint hyperbolic operator with a vector field and an electric potential that depend not only on the space variable but also on the time variable. More precisely, we attempt to stably and…

Analysis of PDEs · Mathematics 2018-10-05 Mourad Bellassoued , Ibtissem Ben Aïcha

The characterization problem of the existence of an unknown obstacle behind a known obstacle is considered by using a singe observed wave at a place where the wave is generated. The unknown obstacle is invisible from the place by using…

Analysis of PDEs · Mathematics 2020-01-27 Masaru Ikehata

We consider inverse boundary value problems for elliptic equations of second order of determining coefficients by Dirichlet-to-Neumann map on subboundaries, that is, the mapping from Dirichlet data supported on $\partial\Omega\setminus…

Mathematical Physics · Physics 2013-03-12 Oleg Yu Imanuvilov , M. Yamamoto