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We consider an inverse boundary value problem for a nonlinear elastic wave equation which was studied in [de Hoop, Uhlmann, Wang. Math. Ann. (2019) doi:10.1007/s00208-018-01796-y]. We show that all the parameters appearing in the equation…

Analysis of PDEs · Mathematics 2021-01-15 Gunther Uhlmann , Jian Zhai

The linear Boltzmann equation governs the absorption and scattering of a population of particles in a medium with an ambient field, represented by a Riemannian metric, where particles follow geodesics. In this paper, we study the possible…

Analysis of PDEs · Mathematics 2023-05-16 Zouhour Rezig

We introduce a time-dimensional reduction method for the inverse source problem in linear elasticity, where the goal is to reconstruct the initial displacement and velocity fields from partial boundary measurements of elastic wave…

Numerical Analysis · Mathematics 2025-06-17 Trong D. Dang , Chanh V. Le , Khoa D. Luu , Loc H Nguyen

In this article we study the inverse problem of recovering a space-dependent coefficient of the Moore-Gibson-Thompson (MGT) equation, from knowledge of the trace of the solution on some open subset of the boundary. We obtain the Lipschitz…

Analysis of PDEs · Mathematics 2021-11-08 Rogelio Arancibia , Rodrigo Lecaros , Alberto Mercado , Sebastián Zamorano

In this paper, we present an inverse problem of identifying the reaction coefficient for time fractional diffusion equations in two dimensional spaces by using boundary Neumann data. It is proved that the forward operator is continuous with…

Numerical Analysis · Mathematics 2018-06-14 Xiaoyan Song , Guanghui Zheng , Lijian Jiang

We consider the following inverse problem: Suppose a $(1+1)$-dimensional wave equation on $\mathbb{R}_+$ with zero initial conditions is excited with a Neumann boundary data modelled as a white noise process. Given also the Dirichlet data…

Analysis of PDEs · Mathematics 2026-01-19 Emilia L. K. Blåsten , Tapio Helin , Antti Kujanpää , Lauri Oksanen , Jesse Railo

We consider an inverse boundary value problem for the heat equation with a nonsmooth coefficient of conductivity which models the displacement of a moving body inside a nonhomogeneous background. We prove the uniqueness of the moving…

Analysis of PDEs · Mathematics 2022-01-24 Olivier Poisson

Given a smooth non-trapping compact manifold with strictly con- vex boundary, we consider an inverse problem of reconstructing the manifold from the scattering data initiated from internal sources. This data consist of the exit directions…

Differential Geometry · Mathematics 2018-03-20 Matti Lassas , Teemu Saksala , Hanming Zhou

We address the nonlinear inverse source problem of identifying a time-dependent source occurring in one node of a network governed by a wave equation. We prove that time records of the associated state taken at a strategic set of two nodes…

Optimization and Control · Mathematics 2019-05-22 J. G. Caputo , A. Hamdi , A. Knippel

A generalized variant of the Calder\'on problem from electrical impedance tomography with partial data for anisotropic Lipschitz conductivities is considered in an arbitrary space dimension $n \geq 2$. The following two results are shown:…

Spectral Theory · Mathematics 2012-05-22 Jussi Behrndt , Jonathan Rohleder

We study the inverse boundary problem for a nonlinear magnetic Schr\"odinger operator on a conformally transversally anisotropic Riemannian manifold of dimension $n\ge 3$. Under suitable assumptions on the nonlinearity, we show that the…

Analysis of PDEs · Mathematics 2023-10-25 Katya Krupchyk , Gunther Uhlmann

Several applications in medical imaging and non-destructive material testing lead to inverse elliptic coefficient problems, where an unknown coefficient function in an elliptic PDE is to be determined from partial knowledge of its…

Optimization and Control · Mathematics 2022-12-13 Bastian Harrach

We study partial data inverse problems for linear and nonlinear parabolic equations with unknown time-dependent coefficients. In particular, we prove uniqueness results for partial data inverse problems for semilinear reaction-diffusion…

Analysis of PDEs · Mathematics 2024-06-04 Ali Feizmohammadi , Yavar Kian , Gunther Uhlmann

We study inverse boundary problems for first order perturbations of the biharmonic operator on a conformally transversally anisotropic Riemannian manifold of dimension $n \ge 3$. We show that a continuous first order perturbation can be…

Analysis of PDEs · Mathematics 2020-12-29 Lili Yan

We consider for the full time-dependent Maxwell's equations the inverse problem of identifying locations and certain properties of small electromagnetic inhomogeneities in a homogeneous background medium from dynamic boundary measurements…

Analysis of PDEs · Mathematics 2009-12-08 C. Daveau , A. Khelifi

We consider the inverse problem of recovering an isotropic quasilinear conductivity from the Dirichlet-to-Neumann map when the conductivity depends on the solution and its gradient. We show that the conductivity can be recovered on an open…

Analysis of PDEs · Mathematics 2019-10-18 Ravi Shankar

We consider inverse problems of determining coefficients or time independent factors of source terms in radiative transport equations by means of Carleman estimate. We establish global Lipschitz stability results with an additional…

Analysis of PDEs · Mathematics 2020-09-10 Manabu Machida , Masahiro Yamamoto

This work concerns inverse boundary value problems for the time-harmonic Maxwell's equations on differential $1-$forms. We formulate the boundary value problem on a $3-$dimensional compact and simply connected Riemannian manifold $M$ with…

Analysis of PDEs · Mathematics 2023-03-14 Sean Holman , Vasiliki Torega

We investigate inverse boundary problems associated with a time-dependent semilinear hyperbolic equation, where both nonlinearity and sources (including initial displacement and initial velocity) are unknown. We establish in several generic…

Analysis of PDEs · Mathematics 2023-03-10 Yi-Hsuan Lin , Hongyu Liu , Xu Liu

Inverse problem for multi-term fractional parabolic equation in two dimensional space, involving m + 1 Caputo fractional derivatives in time, is investigated. Presence of nonlocal boundary conditions leads to a non-self-adjoint spectral…

Analysis of PDEs · Mathematics 2022-02-08 Muhammad Ali , Sara Aziz