Recovery of time-dependent coefficients from boundary data for hyperbolic equations

A Feizmohammadi, J Ilmavirta, Y Kian… - Journal of Spectral …, 2021 - ems.press
We study uniqueness of the recovery of a time-dependent magnetic vector valued potential
and an electric scalar-valued potential on a Riemannian manifold from the knowledge of the …

Uniqueness to some inverse source problems for the wave equation in unbounded domains

G Hu, Y Kian, Y Zhao - Acta Mathematicae Applicatae Sinica, English …, 2020 - Springer
This paper is concerned with inverse acoustic source problems in an unbounded domain
with dynamical boundary surface data of Dirichlet kind. The measurement data are taken at …

Uniqueness of inverse source problems for general evolution equations

Y Kian, Y Liu, M Yamamoto - Communications in Contemporary …, 2023 - World Scientific
In this paper, we investigate inverse source problems for a wide range of PDEs of parabolic
and hyperbolic types as well as time-fractional evolution equations by partial interior …

Partial data inverse problem for hyperbolic equation with time-dependent damping coefficient and potential

B Liu, T Saksala, L Yan - SIAM Journal on Mathematical Analysis, 2024 - SIAM
We study an inverse problem of determining a time-dependent damping coefficient and
potential appearing in the wave equation in a compact Riemannian manifold of dimension …

Identification of unbounded electric potentials through asymptotic boundary spectral data

M Bellassoued, Y Kian, Y Mannoubi… - Research in the …, 2024 - Springer
We prove that the real-valued electric potential q∈ L max (2, 3 n/5)(Ω) of the Dirichlet
Laplacian-Δ+ q acting in a bounded domain Ω⊂ R n, n≥ 3, is uniquely determined by the …

Recovery of nonsmooth coefficients appearing in anisotropic wave equations

A Feizmohammadi, Y Kian - SIAM Journal on Mathematical Analysis, 2019 - SIAM
We study the problem of unique recovery of a nonsmooth one-form A and a scalar function q
from the Dirichlet to Neumann map, A,q, of a hyperbolic equation on a Riemannian manifold …

Determination of singular time-dependent coefficients for wave equations from full and partial data

G Hu, Y Kian - arXiv preprint arXiv:1706.07212, 2017 - arxiv.org
We study the problem of determining uniquely a time-dependent singular potential $ q $,
appearing in the wave equation $\partial_t^ 2u-\Delta_x u+ q (t, x) u= 0$ in $ Q=(0 …

A Borg–Levinson theorem for magnetic Schrödinger operators on a Riemannian manifold

M Bellassoued, M Choulli… - Annales de l'Institut …, 2021 - numdam.org
We establish uniqueness and stability results for the inverse spectral problem of recovering
the magnetic field and the electric potential in a Riemannian manifold from the knowledge of …

Quantitative strong unique continuation for elliptic operators--application to an inverse spectral problem

M Choulli - arXiv preprint arXiv:2209.09549, 2022 - arxiv.org
Based on the three-ball inequality and the doubling inequality established in [24], we
quantify the strong unique continuation for an elliptic operator with unbounded lower order …

[PDF][PDF] Stability of determining a Dirichlet-Laplace-Beltrami operator from its boundary spectral data

M Choulli, M Yamamoto - arXiv preprint arXiv:2311.18642, 2023 - researchgate.net
arXiv:2311.18642v1 [math.AP] 30 Nov 2023 Page 1 arXiv:2311.18642v1 [math.AP] 30 Nov 2023
STABILITY OF DETERMINING A DIRICHLET-LAPLACE-BELTRAMI OPERATOR FROM ITS …