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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

We consider two inverse boundary value problems for the time-harmonic Maxwell equations in an infinite slab. Assuming that tangential boundary data for the electric and magnetic fields at a fixed frequency is available either on subsets of…

Analysis of PDEs · Mathematics 2018-06-25 Monika Pichler

We study the wave equation on a bounded domain of $\mathbb R^m$ and on a compact Riemannian manifold $M$ with boundary. We assume that the coefficients of the wave equation are unknown but that we are given the hyperbolic…

Analysis of PDEs · Mathematics 2020-09-23 Anna Kirpichnikova , Jussi Korpela , Matti Lassas , Lauri Oksanen

We study an inverse problem for nonlinear elliptic equations modelled after the p-Laplacian. It is proved that the boundary values of a conductivity coefficient are uniquely determined from boundary measurements given by a nonlinear…

Analysis of PDEs · Mathematics 2011-06-22 Mikko Salo , Xiao Zhong

We consider an inverse boundary value problem for Maxwell's equations, which aims to recover the electromagnetic material properties of a body from measurements on the boundary. We show that a Lipschitz continuous conductivity, electric…

Analysis of PDEs · Mathematics 2018-07-11 Monika Pichler

The diffraction of a plane wave by a transversely inhomogeneous isotropic nonmagnetic linearly polarized dielectric layer filled with a Kerr-type nonlinear medium is considered. The analytical and numerical solution techniques are…

Analysis of PDEs · Mathematics 2009-10-13 Yury Shestopalov , Vasil Yatsyk

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

We consider the inverse source problem of determining a source term depending on both time and space variable for fractional and classical diffusion equations in a cylindrical domain from boundary measurements. With suitable boundary…

Analysis of PDEs · Mathematics 2020-01-08 Yavar Kian , Masahiro Yamamoto

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

The paper studies inverse problems of determining unknown coefficients in various semi-linear and quasi-linear wave equations. We introduce a method to solve inverse problems for non-linear equations using interaction of three waves, that…

Analysis of PDEs · Mathematics 2023-05-10 Ali Feizmohammadi , Matti Lassas , Lauri Oksanen

In this study, we consider the numerical solution of the Neumann initial boundary value problem for the wave equation in 2D domains. Employing the Laguerre transform with respect to the temporal variable, we effectively transform this…

Numerical Analysis · Mathematics 2023-11-20 Roman Chapko , Leonidas Mindrinos

In this work we investigate an inverse problem of recovering a time-dependent potential in a semilinear subdiffusion model from an integral measurement of the solution over the domain. The model involves the Djrbashian--Caputo fractional…

Numerical Analysis · Mathematics 2023-11-07 Bangti Jin , Kwancheol Shin , Zhi Zhou

We consider the inverse problem of determining the Lam\'{e} parameters and the density of a three-dimensional elastic body from the local time-harmonic Dirichlet-to-Neumann map. We prove uniqueness and Lipschitz stability of this inverse…

Analysis of PDEs · Mathematics 2014-12-12 Elena Beretta , Maarten V. de Hoop , Elisa Francini , Sergio Vessella , Jian Zhai

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 consider the stability in the inverse problem consisting of the determination of a time-dependent coefficient of order zero $q$, appearing in a Dirichlet initial-boundary value problem for a wave equation $\partial_t^2u-\Delta…

Analysis of PDEs · Mathematics 2016-02-01 Yavar Kian

In this paper, we study the inverse boundary value problem for the wave equation with a view towards an explicit reconstruction procedure. We consider both the anisotropic problem where the unknown is a general Riemannian metric smoothly…

Analysis of PDEs · Mathematics 2017-10-10 Maarten de Hoop , Paul Kepley , Lauri Oksanen

In this article we consider an inverse boundary value problem for the time-harmonic Maxwell equations. We show that the electromagnetic material parameters are determined by boundary measurements where part of the boundary data is measured…

Analysis of PDEs · Mathematics 2015-02-06 Francis J. Chung , Petri Ola , Mikko Salo , Leo Tzou

We give a way to recover time-dependent singular coefficients of the wave-equation in the one-dimensional case.

Analysis of PDEs · Mathematics 2019-02-08 Olivier Poisson

In this paper, we investigate the direct and linear inverse problems of identifying time-dependent and time-independent source terms in a time-fractional diffusion-wave equation, using measured data at an interior point of the time…

Analysis of PDEs · Mathematics 2025-08-11 Rahmonov Askar Ahmadovich

We consider the restricted Dirichlet-to-Neumann map $\Lambda^{U,V}_{g,A,q}$ for the wave equation with magnetic potential $A$ and scalar potential $q$, on an admissible Lorentzian manifold $(M, g)$ of dimension $n \geq 3$ with boundary.…

Analysis of PDEs · Mathematics 2025-05-21 Yuchao Yi , Yang Zhang