Publication
My recent research has been focused on inverse problems for elliptic equations and the kinetic theory, that are motivated by applications, such as optical tomography, electrical impedance tomography (EIT), plasma physics and many others.
What are Inverse problems? They are the inverse to the classical direct problems. While one aims to find the unique effect (solution) of a given cause in the direct problems, the inverse problems can be interpreted as finding the cause of a given effect or specifying the model from certain given information of effect. The objectives of inverse problems involve but not limited to the reconstruction of the internal characteristics of an inaccessible region from the boundary measurements as well as the determination of coefficients appearing in the underlying equations from the input and output measurements.
Reconstruction of the Doping Profile in Vlasov-Poisson (with Qin Li and Weiran Sun). Preprint available at arXiv:2401.04834 (2024).
Stable determination of time-dependent collision kernel in the nonlinear Boltzmann equation (with Lili Yan). Preprint available at arXiv:2309.03368 (2023).:2
Partial data inverse problems for the nonlinear Schrödinger equation. (with Xuezhu Lu and Ting Zhou). Accepted in SIAM J. Math. Anal.. Preprint available at arXiv:2306.15935 (2023).:2
Recovery of coefficients in semilinear transport equations. (with Gunther Uhlmann and Hanming Zhou). Accepted in Arch. Rational Mech. Anal.. Preprint available at arXiv:2207.10194 (2022).
Single pixel X-ray transform and related inverse problems. (with Gunther Uhlmann, Jian Zhai and Hanming Zhou), SIAM Journal on Imaging Sciences, 15(4), DOI:10.1137/21M146810 (2022).
Inverse transport and diffusion problems in photoacoustic imaging with nonlinear absorption. (with Kui Ren and Ting Zhou), SIAM Applied Mathematics, 82(2), DOI: 10.1137/21M1436178 (2022).
Inverse source problems in transport equations with external forces. (with Hanming Zhou), Journal of Differential Equations, Vol. 302, No. 25, 728-752, (2021).
An inverse problem for non-linear fractional magnetic Schrödinger equation. (with Ting Zhou), Journal of Differential Equations, 343(15), 64-89 (2023).
Inverse problems for the fractional Laplace equation with lower order nonlinear perturbations. (with Laurel Ohm), Inverse Problems and Imaging,16(2), 305-323, (2022).
Unique determination for an inverse problem from the vortex dynamics. (with Hanming Zhou), Inverse Problems, 37(2), 025001 (2021).
Partial data inverse problems for nonlinear magnetic Schrödinger equations. (with Ting Zhou), Mathematical Research Letters, 30(5), 1535-1563 (2023).
Reconstruction of the emission coefficient in the nonlinear radiative transfer equation. (with C. Klingenberg and Q. Li), SIAM Applied Mathematics, 81(1), 91-106 (2021).
Inverse problems for fractional semilinear elliptic equations. (with Y.-H. Lin), Nonlinear Analysis, Vol. 216, 112699, (2022).
Reconstruction of the collision kernel in the nonlinear Boltzmann equation. (with G. Uhlmann and Y. Yang), SIAM J. Math. Anal., 53(1), 1049-1069 (2021).
On diffusive scaling in acousto-optic imaging. (with F. Chung and Q. Li), Inverse Problems, 36(8), 085011 (2020).
The Calderón problem for a space-time fractional parabolic equation. (with Y.-H. Lin and A. Rüland), SIAM J. Math. Anal., 52(3), 2655-2688 (2020).
Parameter reconstruction for general transport equation. (with Q. Li), SIAM J. Math. Anal., 52(3), 2734-2758 (2020).
Boundary determination of electromagnetic and Lamé parameters with corrupted data. (with P. Caro, Y.-H. Lin and T. Zhou), Inverse Problems and Imaging, 15(5), 1171-1198, (2021)
Inverse problems for the stationary transport equation in the diffusion scaling. (with Q. Li and G. Uhlmann), SIAM Applied Mathematics, 79(6), 2340–2358 (2019).
Global uniqueness for the fractional semilinear Schrödinger equation. (with Y.-H. Lin), Proceedings of the AMS, 147, 1189-1199 (2019).
Quench detection on a superconducting radio-frequency cavity. (with D. Spirn), SIAM Applied Mathematics, 79(1), 341-355 (2019).
Nonparaxial near-nondiffracting accelerating optical beams. (with T. Zhou), Communications in Mathematical Physics, 353(2), 771-790 (2017).
An inverse problem from condense matter physics. (with R. Shankar, D. Spirn and G. Uhlmann), Inverse problems, 33(11), 115011 (2017).
Applications of CGO solutions on coupled-physics inverse problems. (with I. Kocyigit, L. Qiu, Y. Yang and T. Zhou), Inverse problems and imaging, 11(2), 277-304 (2017).
Increasing stability for the conductivity and attenuation coefficients. (with V. Isakov and J.-N. Wang), SIAM J. Math. Anal., 48(1), 569-594 (2016).
Inverse boundary value problem for the Stokes and the Navier-Stokes equations in the plane. (with G. Uhlmann and J.-N. Wang), Arch. Rational Mech. Anal., 215(3), 811-829 (2015).
Uniqueness and stability of Lamé parameters in elastography. Journal of Spectral Theory, 4, 841-877 (2014).
Stability estimates for the inverse boundary value problem by partial Cauchy data. Math. Meth. Appl. Sci., 38(8), 1568-1581 (2015).
Increasing stability for the diffusion equation. Inverse Problems, 30, 075010 (2014).
Global uniqueness for an inverse problem for the magnetic Schrödinger operator. Inverse Problems and Imaging, 5, 59-74 (2011).