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We consider the inverse problem of determining a potential in a semilinear elliptic equation from the knowledge of the Dirichlet-to-Neumann map. For bounded Euclidean domains we prove that the potential is uniquely determined by the…

Analysis of PDEs · Mathematics 2022-02-22 Mikko Salo , Leo Tzou

This paper addresses the inverse problem of simultaneously recovering multiple unknown parameters for semilinear wave equations from boundary measurements. We consider an initial-boundary value problem for a wave equation with a general…

Analysis of PDEs · Mathematics 2026-05-28 Dong Qiu , Xiang Xu , Yeqiong Ye , Ting Zhou

This paper is concerned with the detection of objects immersed in anisotropic media from boundary measurements. We propose an accurate approach based on the Kohn-Vogelius formulation and the topological sensitivity analysis method. The…

Analysis of PDEs · Mathematics 2017-07-13 Maatoug Hassine , Imen Kallel

Based upon elements of the modern Pseudoanalytic Function Theory, we analyse a new method for numerically approaching the solution of the Dirichlet boundary value problem, corresponding to the two-dimensional Electrical Impedance Equation.…

Mathematical Physics · Physics 2012-02-23 M. P. Ramirez T. , C. M. A. Robles G. , R. A. Hernandez-Becerril

In this work we propose a new kind of parameterized outer estimate of the united solution set to an interval parametric linear system. The new method has several advantages compared to the methods obtaining parameterized solutions…

Numerical Analysis · Mathematics 2020-04-02 Evgenija D. Popova

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

The problem of identifying the set of Dirichlet-to-Neumann (DtN) maps arising from conductivities on a smooth domain, among operators acting on functions on the boundary, is a challenging issue in the mathematical analysis of the Calder\'on…

Numerical Analysis · Mathematics 2026-03-17 Carlos Castro , Fabricio Macià , Cristóbal Meroño , Daniel Sánchez-Mendoza

The problem of recovering coefficients in a diffusion equation is one of the basic inverse problems. Perhaps the most important term is the one that couples the length and time scales and is often referred to as {\it the\/} diffusion…

Analysis of PDEs · Mathematics 2021-01-19 Barbara Kaltenbacher , William Rundell

We consider the problem to reconstruct a wave speed $c \in C^\infty(M)$ in a domain $M \subset \R^n$ from acoustic boundary measurements modelled by the hyperbolic Dirichlet-to-Neumann map $\Lambda$. We introduce a reconstruction formula…

Analysis of PDEs · Mathematics 2012-10-04 Shitao Liu , Lauri Oksanen

We give formulae that yield an information about the location of an unknown polygonal inclusion having unknown constant conductivity inside a known conductive material having known constant conductivity from a partial knowledge of the…

Analysis of PDEs · Mathematics 2019-02-15 Masaru Ikehata

First, we obtain a new formula for Bremermann type upper envelopes, that arise frequently in convex analysis and pluripotential theory, in terms of the Legendre transform of the convex- or plurisubharmonic-envelope of the boundary data.…

Analysis of PDEs · Mathematics 2016-07-05 Tamás Darvas , Yanir A. Rubinstein

We consider an inverse problem arising in nonlinear ultrasound imaging. The propagation of ultrasound waves is modeled by a quasilinear wave equation. We make measurements at the boundary of the medium encoded in the Dirichlet-to-Neumann…

Analysis of PDEs · Mathematics 2022-03-08 Gunther Uhlmann , Yang Zhang

A mathematical method for through-wall imaging via wave phenomena in the time domain is introduced. The method makes use of a single reflected wave over a finite time interval and gives us a criterion whether a penetrable obstacle exists or…

Analysis of PDEs · Mathematics 2018-03-06 Masaru Ikehata

We consider the inverse boundary value problem of determining the Lam\'e moduli of an isotropic, static elasticity equations of system at the boundary from the localized Dirichlet-to-Neumann map. Assuming appropriate local regularity…

Analysis of PDEs · Mathematics 2017-11-22 Yi-Hsuan Lin , Gen Nakamura

We introduce and elaborate a novel formalism for the manipulation and analysis of proofs as objects in a global manner. In this first approach the formalism is restricted to first-order problems characterized by condensed detachment. It is…

Logic in Computer Science · Computer Science 2024-10-31 Christoph Wernhard , Wolfgang Bibel

The wave equation is time-reversal invariant. The enclosure method using a Neumann data generated by this invariance is introduced. The method yields the minimum ball that is centered at a given arbitrary point and encloses an unknown…

Analysis of PDEs · Mathematics 2021-03-16 Masaru Ikehata

In this paper, we consider the initial-boundary value problems with several fundamental boundary conditions (the Dirichlet/Neumann/Robin boundary condition) for the multi-component system of semi-linear classical damped wave equations…

Analysis of PDEs · Mathematics 2022-01-25 Tuan Anh Dao , Masahiro Ikeda

For arbitrary values of a parameter $\lambda\in R$, finite-time blow-up of solutions to the generalized, inviscid Proudman-Johnson equation is studied via a direct approach which involves the derivation of representation formulae for…

Analysis of PDEs · Mathematics 2013-08-07 Alejandro Sarria , Ralph Saxton

A positive function (conductivity) on the edges of a graph induces the Dirichlet-to- Neumann map between boundary values of harmonic functions. The inverse conductivity problem is to find the conductivity from the Dirichlet-to-Neumann map.…

General Mathematics · Mathematics 2010-03-05 David V. Ingerman

We study the inverse problem of recovering the spatial support of parameter variations in a system of partial differential equations (PDEs) from boundary measurements. A reconstruction method is developed based on the monotonicity…

Optimization and Control · Mathematics 2025-05-29 Houcine Meftahi , Chayma Nssibi
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