Panrui Ni

Panrui Ni

Post-doc at U Tokyo

CV

Education

Oct. 2024 – Present: Postdoc, Graduate School of Mathematical Sciences, The University of Tokyo, Tokyo, Japan. Mentor: Hiroyoshi Mitake.

Oct. 2023 – Sep. 2024: Postdoc, IMJ-PRG, Paris, France. Mentor: Maxime Zavidovique.

Sep. 2018 – Jun. 2023: PhD, Fudan University, Shanghai, China. Major: Mathematics.

Thesis title: Viscosity solutions of contact-type Hamilton-Jacobi equations. You can find my thesis here. Advisor: Jun Yan.

Sep. 2014 – Jun. 2018: Bachelor, Southeast University, Nanjing, China. Major: Engineering Mechanics.

Thesis title: Variational principle for contact Hamiltonian systems and its applications. Advisor: Changwen Mi.

Publications

  1. Quantitative homogenization of convex Hamilton-Jacobi equations with Neumann type boundary conditions (with H. Mitake), Calculus of Variations and Partial Differential Equations, (2026) 65:154. link
  2. Rate of convergence for homogenization of nonlinear weakly coupled Hamilton-Jacobi systems (with H. Mitake), Journal of Differential Equations, 440 (2025) 113442.
  3. Nonlinear and degenerate discounted approximation in discrete weak KAM theory (with M. Zavidovique), Mathematische Zeitschrift (2025) 310:63 link.
  4. Multiple asymptotic behaviors of solutions in the generalized vanishing discount problem, Proceedings of the American Mathematical Society, Volume 151, Pages 5239 – 5250, 2023. link
  5. Time periodic solutions of first order mean field games from the perspective of Mather theory, Journal of Differential Equations, Volume 412, Pages 881 – 901, 2024. link
  6. Weakly coupled Hamilton-Jacobi systems without monotonicity condition: A first step, Communications on Pure and Applied Analysis, Volume 23, Issue 7, Pages 961 – 983, 2024. link
  7. A nonlinear semigroup approach to Hamilton-Jacobi equations–revisited (with L. Wang), Journal of Differential Equations, 403, 272 – 307, 2024. link
  8. Aubry-Mather theory for contact Hamiltonian systems III (with L. Wang), Science China Mathematics, Volume 67, pages 2541 – 2570, 2024. link
  9. Viscosity solutions of contact Hamilton-Jacobi equations with Hamiltonians depending periodically on unknown functions (with K. Wang and J. Yan), Communications on Pure and Applied Analysis, Volume 22, Issue 2, Pages 668 – 685, 2023. link
  10. A weakly coupled mean field games model of first order for k groups of major players (with K. Wang and J. Yan), Proceedings of the American Mathematical Society, published online. link
  11. A representation formula of the viscosity solution of the contact Hamilton-Jacobi equation and its application (with L. Wang and J. Yan), Chinese Annals of Mathematics, Series B, Volume 46, Pages 449 – 480, 2025. link
  12. On variation of action integral in Finsler gravity (with B. Shen), Annals of Physics, Volume 404, Issue 1, Pages 93 – 114, 2019. link

Preprints

  1. Static class-guided selection of elementary solutions in non-monotone vanishing discount problems (with J. Yan and M. Zavidovique). link
  2. Quantitative homogenization of first-order ODEs. link
  3. Quantitative homogenization of convex Hamilton-Jacobi equations with u/ε-periodic Hamiltonians (with H. Mitake and H. V. Tran). link
  4. Convergence/divergence phenomena in the vanishing discount limit of Hamilton-Jacobi equations (with A. Davini, J. Yan and M. Zavidovique). link

Awards

  1. Award of Outstanding Graduate of Shanghai, Shanghai Municipal Education Commission, 2023.
  2. “Qinghua” Scholarship, Fudan University, 2020-2021.
  3. Academic Scholarships for PhD Degree Students, Fudan University, 2020.
  4. Excellent Student of Fudan University, Fudan University, 2018-2019.
  5. National Scholarship, The Ministry of Education of the People’s Republic of China, 2017 and 2019.

Conference Activities

Nov. 2025: Viscosity Solutions of Differential Equations and Related Topics, RIMS, Kyoto University. Title: Quantitative Homogenization of Convex Hamilton-Jacobi Equations with u/ε-Periodic Hamiltonians.

Jun. 2025: Recent progress in Hamilton-Jacobi equations and related topics, Nanjing University. Title: Convergence/divergence phenomena in the vanishing discount limit of Hamilton-Jacobi equations.

Jan. 2024: ANR meeting, École normale supérieure de Lyon, Invited speaker. Title: On discrete nonlinear vanishing discount problem.

Jul. 2022: Conference on Differential Equations and Dynamical Systems, Beijing Institue of Technology, Invited speaker. Title: A nonlinear semigroup approach to a class of nonmonotone Hamilton-Jacobi equations.

Teaching Activities

Sep. 2020 – Jan. 2021: Teaching assistant in Fudan University, Course: Classical Mechanics.

Feb. 2019 – Jun. 2019: Teaching assistant in Fudan University, Course: Classical Mechanics.