Publications

  • Recently, my research is mainly focused on inverse problems for linear, nonlinear, nonlocal (integral) differential equations, and their interactions. The study of inverse problems is a branch of applied mathematics that investigates indirect boundary or exterior measurements. Most of these mathematical studies are inspired by applications, such as electrial impedance tomography (EIT), computerized tomography (CT) and invisible cloaking.
  • InverseProblems
  • My preprints or accepted manuscripts can be found below in pdf form. The final version of these articles can be changed after publication, so please read them in the indicated journals if necessary. You can also find my preprints in terms of chronological records via arXiv. Besides, you might be interested to see my MathScinet and Google Scholar related to my research outputs.

Preprints/Submitted Papers
  1. (with P. Zimmermann) On uniqueness in nonlocal diffuse optical tomography
    submitted (2024), arXiv:2406.06226. [arXiv]
  2. Determining both leading coefficient and source in a nonlocal elliptic equation
    submitted (2023), arXiv:2312.15607. [arXiv]
  3. (with C.-L. Lin and G. Uhlmann) The Calderón problem for nonlocal parabolic operators: A new reduction from the nonlocal to the local
    submitted (2023), arXiv:2308.09654. [arXiv]
  4. (with P. Zimmermann) Unique determination of coefficients and kernel in nonlocal porous medium equations with absorption term
    submitted (2023), arXiv:2305.16282. [arXiv]
  5. (with J. Railo and P. Zimmermann) The Calderón problem for a nonlocal diffusion equation with time-dependent coefficients
    submitted (2022), arXiv:2211.07781. [arXiv]
  6. (with C.-L. Lin and G. Uhlmann) The Calderón problem for nonlocal parabolic operators
    submitted (2022), arXiv:2209.11157. [arXiv]

Published/Accepted Papers
  1. (with M. Kar and P. Zimmermann) Determining coefficients for a fractional p-Laplace equation from exterior measurements
    J. Differential Equations, accepted for publication. [arXiv]
  2. (with T. Tyni and P. Zimmermann) Well-posedness and inverse problems for semilinear nonlocal wave equations
    Nonlinear Anal., accepted for publication. [arXiv]
  3. (with T. Liimatainen) Uniqueness results for inverse source problems of semilinear elliptic equations
    Inverse Problems, Vol. 40, No. 4 (2024), 045030, 1-32.
  4. [Journal] [arXiv]
  5. (with Y. Kian and T. Liimatainen) On determining and breaking the gauge class in inverse problems for reaction-diffusion equations
    Forum Math. Sigma, Vol. 12, e25 (2024), 1-42.
  6. [Journal] [arXiv]
  7. (with H. Liu and X. Liu) Determining a nonlinear hyperbolic system with unknown sources and nonlinearity
    J. Lond. Math. Soc., Vol. 109, Issue 2, e12865 (2024), 1-39.
  8. [Journal] [arXiv]
  9. (with A. Feizmohammadi and T. Liimatainen) An inverse problem for a semilinear elliptic equation on conformally transversally anisotropic manifolds
    Ann. PDE, Vol. 9, Article number: 12 (2023), 1-54.
  10. [Journal] [arXiv]
  11. (with H. Liu) Inverse problems for fractional equations with a minimal number of measurements
    Comm. Anal. Comp., Vol. 1 (2023), 72-93.
  12. [Journal] [arXiv]
  13. (with B. Harrach) Simultaneous recovery of piecewise analytic coefficients in a semilinear elliptic equation
    Nonlinear Anal., Vol. 228 (2023), 113188, 1-14.
  14. [Journal] [arXiv]
  15. (with H. Liu, X. Liu and S. Zhang) Simultaneous recoveries for semilinear parabolic systems
    Inverse Problems, Vol. 38, No. 11 (2022), 115006, 1-39.
  16. [Journal] [arXiv]
  17. Monotonicity-based inversion of fractional semilinear elliptic equations with power type nonlinearities
    Cal. Var. Partial Differential Equations, Vol. 61, Article number: 188 (2022), 1-30.
  18. [Journal] [arXiv]
  19. (with P.-Z. Kow and J.-N. Wang) The Calderón problem for the fractional wave equation: Uniqueness and optimal stability
    SIAM J. Math Anal., Vol. 54, Issue 3 (2022), 3379-3419.
  20. [Journal] [arXiv]
  21. (with R.-Y. Lai) Inverse problems for fractional semilinear elliptic equations
    Nonlinear Anal., Vol. 216 (2022), 112699, 1-21.
  22. [Journal] [arXiv]
  23. (with T. Liimatainen, M. Salo, and T. Tyni) Inverse problems for elliptic equations with fractional power type nonlinearities
    J. Differential Equations, Vol. 306, Issue 5 (2022), 189-219.
  24. [Journal] [arXiv]
  25. (with P. Caro, R.-Y. Lai and T. Zhou) Boundary determination of electromagnetic and Lamé parameters with corrupted data
    Inverse Probl. Imaging, Vol. 15, Issue 5 (2021), 1171-1198.
  26. [Journal] [arXiv]
  27. (with M. Lassas, T. Liimatainen and M. Salo) Partial data inverse problems and simultaneous recovery of boundary and coefficients for semilinear elliptic equations
    Rev. Mat. Iberoam., Vol. 37, Issue 4 (2021), 1553–1580.
  28. [Journal] [arXiv]
  29. (with G. Nakamura, R. Potthast and H. Wang) Duality between range and no-response tests and its application for inverse problems
    Inverse Probl. Imaging, Vol. 15, No. 2 (2021), 367-386.
  30. [Journal] [arXiv]
  31. (with M. Lassas, T. Liimatainen and M. Salo) Inverse problems for elliptic equations with power type nonlinearities
    J. Math. Pures Appl., Vol. 145 (2021), 44-82.
  32. [Journal] [arXiv]
  33. (with R. Murthy, K. Shin and J. Mueller) A direct reconstruction algorithm for the anisotropic inverse conductivity problem based on Calderón method in the plane
    Inverse Problems, Vol. 36 (2020), 125008, 1-21.
  34. [Journal] [arXiv]
  35. (with R.-Y. Lai and A. Rüland) The Calderón problem for a space-time fractional parabolic equation
    SIAM J. Math Anal., Vol. 52, Issue 3 (2020), 2655-2688.
  36. [Journal] [arXiv]
  37. (with M. Cekić and A. Rüland) The Calderón problem for the fractional Schrödinger equation with drift
    Cal. Var. Partial Differential Equations, Vol. 59, No. 3 (2020), 1-46.
  38. [Journal] [arXiv]
  39. (with B. Harrach) Monotonicity-based inversion of the fractional Schrödinger equation II. General potentials and stability
    SIAM J. Math Anal., Vol. 52, Issue 1 (2020), 402-436.
  40. [Journal] [arXiv]
  41. (with B. Harrach) Monotonicity-based inversion of the fractional Schrödinger equation I. Positive potentials
    SIAM J. Math Anal., Vol. 51, Issue 4 (2019), 3092-3111.
  42. [Journal] [arXiv]
  43. (with S. Meng) Leading and second order homogenization of an elastic scattering problem for highly oscillating anisotropic medium
    J. Elasticity, Vol. 137, Issue 2 (2019), 177-217.
  44. [Journal] [arXiv]
  45. (with X. Cao and H. Liu) Simultaneously recovering potentials and embedded obstacles for anisotropic fractional Schrödinger operators
    Inverse Probl. Imaging, Vol. 13, Issue 1 (2019), 197-210.
  46. [Journal] [arXiv]
  47. (with R.-Y. Lai) Global uniqueness for the fractional semilinear Schrödinger equation
    Proc. Amer. Math. Soc., Vol. 147, No. 3 (2019), 1189-1199.
  48. [Journal] [arXiv]
  49. (with E. Blåsten) Radiating and non-radiating sources in elasticity
    Inverse Problems, Vol. 35, No. 1 (2019), 1-16.
  50. [Journal] [arXiv]
  51. (with B. Harrach and H. Liu) On localizing and concentrating electromagnetic fields
    SIAM J. Appl. Math, Vol. 78, Issue 5 (2018), 2558-2574.
  52. [Journal] [arXiv]
  53. Nearly cloaking for the elasticity system with residual stress
    Asymptot. Anal., Vol. 106, Issue 1 (2018), 1-23.
  54. [Journal] [arXiv]
  55. (with T. Ghosh and J. Xiao) The Calderón problem for variable coefficient nonlocal elliptic operators
    Comm. Partial Differential Equations, Vol. 42, No. 12 (2017), 1923-1961.
  56. [Journal] [arXiv]
  57. (with G. Nakamura) Boundary determination of the Lamé moduli for the isotropic elasticity system
    Inverse Problems, Vol. 33, No. 12 (2017), 1-23.
  58. [Journal] [arXiv]
  59. Reconstruction of penetrable obstacles in the anisotropic acoustic scatterings
    Inverse Probl. Imaging, Vol. 10, Issue 3 (2016), 765-780.
  60. [Journal] [arXiv]
  61. Strong unique continuation for a residual stress system with Gevrey coefficients
    Proc. Amer. Math. Soc. 144 (2016), 2171-2183.
  62. [Journal] [arXiv]
  63. (with R. Kuan and M. Sini) The enclosure method for the anisotropic Maxwell system
    SIAM J. Math Anal., Vol 47 (2015), 3488-3527.
  64. [Journal] [arXiv]

Other Articles

Collaborators
(35 collaborators in alphabetical order.)
  • Blåsten, Emilia (Associate Professor, LUT School of Engineering, LUT University, Finland)
  • Cao, Xinlin (Research Assistant Professor, Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong)
  • Caro, Pedro (Ikerbasque Research Fellow at Basque Center for Applied Mathematics (BCAM), Spain)
  • Cekić, Mihajlo (SNF Ambizione Fellow, University of Zurich, Switzerland)
  • Feizmohammadi, Ali (Postdoctoral fellow and Lecturer, University of Toronto, Canada)
  • Ghosh, Tuhin (Reader F, Harish-Chandra Research Institute, India)
  • Harrach, Bastian (Professor & Chair of Numerics for Partial Differential Equations, Institute of Mathematics, Goethe University Frankfurt, Germany)
  • Kar, Manas (Assistant Professor, Department of Mathematics, IISER Bhopal, India)
  • Kian, Yavar (Professor, Laboratoire de Mathématiques Raphaël Salem (LMRS), Université de Rouen Normandie, France)
  • Kow, Pu-Zhao (Assistant Professor, Department of Mathematical Sciences, National Chengchi University, Taiwan)
  • Kuan, Rulin (Assistant Professor, Department of Mathematics, National Cheng Kung University, Taiwan)
  • Lai, Ru-Yu (Associate Professor, University of Minnesota, USA)
  • Lassas, Matti (Academy Professor, Department of Mathematics and Statistics, University of Helsinki, Finland)
  • Liimatainen, Tony (Researcher, Department of Mathematics and Statistics, University of Jyväskylä, Finland)
  • Lin, Ching-Lung (Professor, Department of Mathematics, National Cheng Kung University, Taiwan)
  • Liu, Hongyu (Professor, Department of Mathematics, City University of Hong Kong, Hong Kong)
  • Liu, Xu (Professor, School of Mathematics and Statistics, Northeast Normal University, China)
  • Meng, Shixu (Associate Professor, Chinese Academy of Sciences, Academy of Mathematics and Systems Science, China)
  • Muller, Jennifer (Professor, Department of Mathematics, Colorado State University, USA)
  • Murthy, Rashmi (Postdoctoral Fellow, University of Helsinki, Finland)
  • Nakamura, Gen (Professor Emeritus, Hokkaido University, Japan)
  • Potthast, Roland (Director and Professor for Data Assimilation at DWD/DMVI, Germany & Professor in University of Reading, UK)
  • Railo, Jesse (Associate Professor, LUT School of Engineering, LUT University, Finland)
  • Rüland, Angkana (Professor, Institute for Applied Mathematics, Hausdorff Center for Mathematics, University of Bonn, Germany)
  • Salo, Mikko (Professor, Department of Mathematics and Statistics, University of Jyväskylä, Finland)
  • Shin, Kwancheol (Researcher, The Hong Kong Polytechnic University, Hong Kong)
  • Sini, Mourad (Professor, Johann Radon Institute for Computational and Applied Mathematics, Austria)
  • Tyni, Teemu (Assistant Professor, Unit of Applied and Computational Mathematics, University of Oulu, Finland)
  • Uhlmann, Gunther (Walker Family Endowed Professor & IAS Si Yuan Professor , Department of Mathematics, University of Washington & IAS HKUST)
  • Wang, Haibing (Professor, Department of Mathematics, Southeast University, China)
  • Wang, Jenn-Nan (Professor, Institute of Applied Mathematics, National Taiwan University, Taiwan)
  • Xiao, Jingni (Assistant Professor, Department of Mathematics, Drexel University, USA)
  • Zhang, Shen (PhD student, Department of Mathematics, City University of Hong Kong, Hong Kong)
  • Zhou, Ting (Professor, Department of Mathematics, Zhejiang University, China)
  • Zimmermann, Philipp (Postdoctoral Fellow, Departament de Matemàtiques i Informàtica, Universitat de Barcelona, Spain)

PhD Thesis
  • Download, doi: 10.6342, NTU/201600158
  • Slide for the PhD thesis defense

Some Lecture Notes
These notes (only for personal records) might be incorrect or contain errors. Please be careful in using them.
  • Harmonic Analysis course @ NTU, 2016.02-2016.06 PDF
  • NCTS Distinguished Scholar and NTU visiting chair
    • Spectral Graph Theory and its Applications PDF
  • IAS workshop on Inverse Problems, Imaging and PDE
    • Calderon's problem for elliptic system PDF
  • NCTS Summer Courses on Analysis and PDEs
    • Introduction to EIT PDF
    • Classical DeGiorgi method to NS equation PDF
  • NCTS Minicourse on Periodic Homogenization of Elliptic Problems
    • Introduction to elliptic homogenization problem PDF
  • NCTS seminar - The DeGiorgi method and its application to parabolic regularity
    • Vasseur, DeGiorgi method PDF
  • On the inviscid limit problem for incompressible flows in the half-plane
    • Incompressible Navier-Stokes equation PDF
  • NCTS Distinguished Lectures Series (Click Here)
    • Theory and Applications to homogenization - A revisit with recent progress PDF
  • Other Notes:
    • Method of moving plane PDF
    • Dirichlet-Neumann relations PDF
    • Radon transform PDF
    • Liapunov-Schmidt reduction PDF
Copyright © Dr. Yi-Hsuan Lin