Panrui Ni

Panrui Ni

Post-doc at IMJ-PRG

CV

Education

Oct. 2024 – present: Visiting researcher, Graduate School of Mathematical Sciences, The University of Tokyo, Tokyo, Japan. Mentor: Hiroyoshi Mitake.

Oct. 2023 – Sep. 2024: Post-doc, 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. Panrui Ni, Multiple asymptotic behaviors of solutions in the generalized vanishing discount problem, Proceedings of the American Mathematical Society, Volume 151, Pages 5239 – 5250, 2023. link
  2. Panrui Ni, 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
  3. Panrui Ni, 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
  4. Panrui Ni and L. Wang, A nonlinear semigroup approach to Hamilton-Jacobi equations–revisited, Journal of Differential Equations, 403, 272 – 307, 2024. link
  5. Panrui Ni and L. Wang, Aubry-Mather theory for contact Hamiltonian systems III, SCIENCE CHINA Mathematics, published online. link
  6. Panrui Ni, K. Wang, and J. Yan, Viscosity solutions of contact Hamilton-Jacobi equations with Hamiltonians depending periodically on unknown functions, Communications on Pure and Applied Analysis, Volume 22, Issue 2, Pages 668 – 685, 2023. link
  7. Panrui Ni, K. Wang, and J. Yan, A weakly coupled mean field games model of first order for k groups of major players, Proceedings of the American Mathematical Society, published online. link
  8. Panrui Ni, L. Wang and J. Yan, A representation formula of the viscosity solution of the contact Hamilton-Jacobi equation and its application, Chinese Annals of Mathematics, Series B, accepted. link
  9. Panrui Ni and B. Shen, On variation of action integral in Finsler gravity, Annals of Physics, Volume 404, Issue 1, Pages 93 – 114, 2019. link

Preprints

  1. H. Mitake, Panrui Ni, Quantitative homogenization of convex Hamilton-Jacobi equations with Neumann type boundary conditions. link
  2. H. Mitake, Panrui Ni, Rate of convergence for homogenization of nonlinear weakly coupled Hamilton-Jacobi systems. link
  3. A. Davini, Panrui Ni, J. Yan and M. Zavidovique, Convergence/divergence phenomena in the vanishing discount limit of Hamilton-Jacobi equations. link
  4. Panrui Ni and M. Zavidovique, Nonlinear and degenerate discounted approximation in discrete weak KAM theory. link
  5. Panrui Ni and L. Wang, On Mather’s Lipschitz graph theorem of the Aubry set for contact Hamiltonian systems, submitted.

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

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.

Jun. 2023: PDE reading seminar online, Invited speaker. Title: Hamilton-Jacobi equations depending Lipschitz continuously on the unknown function. link

Teaching Activities

Feb. 2021 – Jun. 2021: Teaching assistant in Fudan University, Course: Calculus.

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

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