Scholars@Duke
Ying Liang

Ying Liang

Phillip Griffiths Assistant Research Professor of Mathematics
Mathematics

Selected Publications

STABILITY FOR INVERSE RANDOM SOURCE PROBLEMS OF THE POLYHARMONIC WAVE EQUATION

Journal Article Inverse Problems and Imaging · April 1, 2026 This paper investigates stability estimates for inverse source problems in the stochastic polyharmonic wave equation in three dimensions, where the source is represented by white noise. The study examines the well-posedness of the direct problem and derive ... Full text Cite

A rigorous theory on electromagnetic diffraction by a planar aperture in a perfectly conducting screen

Journal Article Journal of Mathematical Physics · July 1, 2024 In this paper, we revisit the classic problem of diffraction of electromagnetic waves by an aperture in a perfectly conducting plane. We formulate the diffraction problem using a boundary integral equation that is defined on the aperture using Dyadic Green ... Full text Cite

A Direct Probing Method of an Inverse Problem for the Eikonal Equation

Journal Article SIAM Journal on Scientific Computing · April 30, 2024 Full text Cite

Stability for Inverse Source Problems of the Stochastic Helmholtz Equation with a White Noise

Journal Article SIAM Journal on Applied Mathematics · April 30, 2024 Full text Cite

A Data-Assisted Two-Stage Method for the Inverse Random Source Problem

Journal Article SIAM Journal on Imaging Sciences · December 31, 2023 Full text Cite

Least-squares method for recovering multiple medium parameters

Journal Article Inverse Problems · December 1, 2022 AbstractWe present a two-stage least-squares method for inverse medium problems of reconstructing multiple unknown coefficients simultaneously from noisy data. A direct sampling method is applied to detect t ... Full text Cite

Mathematical and Numerical Study of a Three-Dimensional Inverse Eddy Current Problem

Journal Article SIAM Journal on Applied Mathematics · January 2020 Full text Cite