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publications
A weakly coupled mean field games model of first order for k groups of major players
Published in Proceedings of the American Mathematical Society, 2022
This paper is about a weakly coupled mean field games model of first order for k groups of major players.
Recommended citation: P. Ni, K. Wang, and J. Yan, A weakly coupled mean field games model of first order for k groups of major players, Proc. Amer. Math. Soc., published online. https://www.ams.org/journals/proc/earlyview/#proc16342
Viscosity solutions of contact Hamilton-Jacobi equations with Hamiltonians depending periodically on unknown functions
Published in Communications on Pure and Applied Analysis, 2023
This paper is about H-J equations with the Hamiltonian periodic in the unknown function.
Recommended citation: P. Ni, K. Wang and J. Yan, Viscosity solutions of contact Hamilton-Jacobi equations with Hamiltonians depending periodically on unknown functions, Comm. Pure Appl. Anal., 22 (2023), 668-685. https://www.aimsciences.org//article/doi/10.3934/cpaa.2023005
Multiple asymptotic behaviors of solutions in the generalized vanishing discount problem
Published in Proceedings of the American Mathematical Society, 2023
This paper is about a counter example for vanishing discount problem when the Hamiltonian is non-monotone in the unknown function.
Recommended citation: P. Ni, Multiple asymptotic behaviors of solutions in the generalized vanishing discount problem, Proc. Amer. Math. Soc. 151 (2023), 5239-5250. https://doi.org/10.1090/proc/16420
A representation formula of the viscosity solution of the contact Hamilton-Jacobi equation and its applications
Published in Chinese Annals of Mathematics, Series B, 2023
This paper is about the implicit solution semigroup for the standard PDE assumptions.
Recommended citation: P. Ni, L. Wang, and J. Yan, A representation formula of the viscosity solution of the contact Hamilton-Jacobi equation and its applications, Chinese Annals of Mathematics, Series B, to appear. https://arxiv.org/abs/2101.00446
Aubry-Mather theory for contact Hamiltonian systems III
Published in SCIENCE CHINA Mathematics, 2023
This paper is about the topological dynamics of the Aubry sets for contact Hamiltonian systems.
Recommended citation: P. Ni and L. Wang, Aubry-Mather theory for contact Hamiltonian systems III, SCIENCE CHINA Mathematics, published online, 2023. https://www.sciengine.com/SCM/doi/10.1007/s11425-022-2197-4
A nonlinear semigroup approach to Hamilton-Jacobi equations–revisited
Published in Journal of Differential Equations, 2024
Recommended citation: P. Ni, L. Wang, A nonlinear semigroup approach to Hamilton-Jacobi equations–revisited, J. Differential Equations, 403 (2024), 272 – 307.
Weakly coupled Hamilton-Jacobi systems without monotonicity condition: A first step
Published in Communications on Pure and Applied Analysis, 2024
Recommended citation: P. Ni, Weakly coupled Hamilton-Jacobi systems without monotonicity condition: A first step, Comm. Pure Appl. Anal., 23 (2024), 961-983.
Time periodic solutions of first order mean field games from the perspective of Mather theory
Published in Journal of Differential Equations, 2024
Recommended citation: P. Ni, Time periodic solutions of first order mean field games from the perspective of Mather theory, J. Differential Equations, 412 (2024), 881-901.
talks
A nonlinear semigroup approach to a class of nonmonotone Hamilton-Jacobi equations
Published:
This talk is based on the article link.
On discrete nonlinear vanishing discount problem
Published:
In this talk, I first introduced a discrete approximation of the implicit solution semigroup. The discrete nonlinear vanishing discount problem will be considered, where the Mather measures play a center role. I will also discuss the uniqueness of the discounted solution. It is a joint work with Maxime Zavidovique.
teaching
Classical Mechanics
Workshop, School of Matthematical Sciences, Fudan University, 2020
The course is Classical Mechanics, and mainly about Lagrangian and Hamiltonian mechanics, calculus of variations and Hamilton-Jacobi equations. The duty of the teaching assistant position is to assist the teacher to carry out orderly teaching work, correct students’ homework, teach exercise classes, and answer questions in a timely manner.
Calculus
Undergraduate course, School of Mathematical Sciences, Fudan University, 2021
The course is Calculus (BII) and mainly about series, multivariable calculus and ordinary differential equations.