Research
Research Interests:
Partial Differential Equations, Applied Mathematics, Traffic Flow Models, Dispersive Water Waves
Google Scholar, GSU Math Physics Seminar
Publications:
[12] Yongki Lee.
An extension of Seliger's wave breaking condition for the nonlocal Whitham type equation, arXiv:2210.13405, 2022
[11] Yongki Lee.
On the Riccati dynamics of 2D Euler-Poisson equations with attractive forcing, Nonlinearity, 2022
[10] Yongki Lee, Changhui Tan.
A sharp critical threshold for a traffic flow model with look-ahead dynamics, Communications in Mathematical Sciences, 2022
[9] Yongki Lee.
Wave breaking in a class of non-local conservation laws, Journal of Differential Equations, 2020
[8] Yongki Lee.
Traffic flow models with looking ahead relaxation and behind intensification, Journal of the Korean Mathematical Society, 2020
[7] Yongki Lee.
Thresholds for shock formation in traffic flow models with nonlocal-concave-convex flux, Journal of Differential Equations, 2019
[6] Yongki Lee.
Upper-thresholds for shock formation in two-dimensional weakly restricted Euler-Poisson equations, Communications in Mathematical Sciences, 2017
[5] Yongki Lee.
Blow-up conditions for two dimensional modified Euler-Poisson equations, Journal of Differential Equations, 2016
[4] Yongki Lee, Hailiang Liu.
Threshold for shock formation in the hyperbolic Keller-Segel model, Applied Mathematics Letters, 2015
[3] Yongki Lee, Hailiang Liu.
Thresholds for shock formation in traffic flow models with Arrhenius look-ahead dynamics(with Hailiang Liu), Discrete and Continuous Dynamical Systems-Series A, 2015
[2] Yongki Lee, Hailiang Liu.
Thresholds in three-dimensional restricted Euler-Poisson equation, Physica D: Nonlinear Phenomena, 2013
[1] Threshold dynamics in hyperbolic partial differential equations. Ph.D. Thesis, Iowa State University, 2014
Preliminary reports:
Global solutions for the two dimensional Euler-Poisson system with attractive forcing, arXiv:2007.07960
On the Riccati dynamics of the Euler-Poisson equations with zero background state, arXiv:2009.00580