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We study an inverse problem for fractional elasticity. In analogy to the classical problem of linear elasticity, we consider the unique recovery of the Lam\'e parameters associated to a linear, isotropic fractional elasticity operator from…

Analysis of PDEs · Mathematics 2022-10-03 Giovanni Covi , Maarten de Hoop , Mikko Salo

We present two uniqueness results for the inverse problem of determining an index of refraction by the corresponding acoustic far-field measurement encoded into the scattering amplitude. The first one is a local uniqueness in determining a…

Analysis of PDEs · Mathematics 2013-08-28 Guanghui Hu , Hongyu Liu

We study the uniqueness question for two inverse problems on graphs. Both problems consist in finding (possibly complex) edge or nodal based quantities from boundary measurements of solutions to the Dirichlet problem associated with a…

Combinatorics · Mathematics 2015-10-13 Justin Boyer , Jack J. Garzella , Fernando Guevara Vasquez

When considering fractional diffusion equation as model equation in analyzing anomalous diffusion processes, some important parameters in the model, for example, the orders of the fractional derivative or the source term, are often unknown,…

Analysis of PDEs · Mathematics 2019-04-15 Zhiyuan Li , Masahiro Yamamoto

We consider a time-independent variable coefficients fractional porous medium equation and formulate an associated inverse problem. We determine both the conductivity and the absorption coefficient from exterior partial measurements of the…

Analysis of PDEs · Mathematics 2023-02-07 Li Li

We first formulate an inverse problem for a linear fractional Lam\'e system. We determine the Lam\'e parameters from exterior partial measurements of the Dirichlet-to-Neumann map. We further study an inverse obstacle problem as well as an…

Analysis of PDEs · Mathematics 2021-09-09 Li Li

We show global uniqueness in the fractional Calder\'on problem with a single measurement and with data on arbitrary, possibly disjoint subsets of the exterior. The previous work \cite{GhoshSaloUhlmann} considered the case of infinitely many…

Analysis of PDEs · Mathematics 2020-02-12 Tuhin Ghosh , Angkana Rüland , Mikko Salo , Gunther Uhlmann

In this work, a novel approach for the solution of the inverse conductivity problem from one and multiple boundary measurements has been developed on the basis of the implication of the framework of BV - functions. The space of the…

Analysis of PDEs · Mathematics 2020-05-20 Antonios Charalambopoulos , Vanessa Markaki , Drosos Kourounis

We prove that an $L^\infty$ potential in the Schr\"odinger equation in three and higher dimensions can be uniquely determined from a finite number of boundary measurements, provided it belongs to a known finite dimensional subspace…

Analysis of PDEs · Mathematics 2019-10-10 Giovanni S. Alberti , Matteo Santacesaria

In this paper we study an inverse problem for fractional anisotropic conductivity. Our nonlocal operator is based on the well-developed theory of nonlocal vector calculus, and differs substantially from other generalizations of the…

Analysis of PDEs · Mathematics 2022-12-23 Giovanni Covi

This paper is concerned with the mathematical analysis of the inverse random source problem for the time fractional diffusion equation, where the source is assumed to be driven by a fractional Brownian motion. Given the random source, the…

Analysis of PDEs · Mathematics 2020-04-22 Xiaoli Feng , Peijun Li , Xu Wang

We consider an inverse boundary value problem for diffusion equations with multiple fractional time derivatives. We prove the uniqueness in determining a number of fractional time-derivative terms, the orders of the derivatives and…

Analysis of PDEs · Mathematics 2019-04-15 Zhiyuan Li , O. Y. Imanuvilov , Masahiro Yamamoto

This paper is devoted to the investigation of inverse problems related to stationary drift-diffusion equations modeling semiconductor devices. In this context we analyze several identification problems corresponding to different types of…

Analysis of PDEs · Mathematics 2020-11-24 M. Burger , H. W. Engl , A. Leitão , P. A. Markowich

We study an inverse problem for the fractional Allen-Cahn equation. Our formulation and arguments rely on the asymptotics for the fractional equation and unique continuation properties.

Analysis of PDEs · Mathematics 2025-08-18 Li Li

In this paper, we consider the inverse scattering problem associated with an inhomogeneous media with a conductive boundary. First, we discuss the inverse conductivity problem of reconstructing the conductivity parameter from scattering…

Analysis of PDEs · Mathematics 2017-12-12 Isaac Harris , Andreas Kleefeld

We prove for a two dimensional bounded domain that the Cauchy data for the Schroedinger equation measured on an arbitrary open subset of the boundary determines uniquely the potential. This implies, for the conductivity equation, that if we…

Analysis of PDEs · Mathematics 2008-10-14 Oleg Y. Imanuvilov , Gunther Uhlmann , Masahiro Yamamoto

We study the well-posedness of a semilinear fractional diffusion equation and formulate an associated inverse problem. We determine fractional power type nonlinearities from the exterior partial measurements of the Dirichlet-to-Neumann map.…

Analysis of PDEs · Mathematics 2022-03-30 Li Li

This paper is concerned with the inverse problem on determining an orbit of the moving source in a fractional diffusion(-wave) equations in a connected bounded domain of $\mathbb R^d$ or in the whole space $\mathbb R^d$. Based on a newly…

Analysis of PDEs · Mathematics 2020-02-06 Guanghui Hu , Yikan Liu , Masahiro Yamamoto

We consider the determination of a conductivity function in a two-dimensional domain from the Cauchy data of the solutions of the conductivity equation on the boundary. We prove uniqueness results for this inverse problem, posed by…

Analysis of PDEs · Mathematics 2016-02-24 Kari Astala , Matti Lassas , Lassi Paivarinta

The aim of the paper is twofold. Firstly, we would like to derive quantitative uniqueness estimates for solutions of the general complex conductivity equation. It is still unknown whether the \emph{strong} unique continuation property holds…

Analysis of PDEs · Mathematics 2018-10-02 Catalin Carstea , Tu Nguyen , Jenn-Nan Wang