Fall 2019

Joint talk with Department Colloquium 

Date: Tuesday, December 3 

Time: 1:00 – 2:00 PM 

Location: TBA

Speaker: Dr. Yi Hu (Georgia Southern University) 

Title: Blowup rate for rotational nonlinear Schrödinger equations (NLS)

Abstract: In this talk we will give a brief introduction to the blowup phenomena and blowup rate of rotational NLS in the mass critical and super-crtical cases. In the mass critical case we will present a log-log blowup rate, and in the super-critical case we will present a universal upper bound for blow up.

Joint talk with Department Colloquium 

• Date: Friday, October 11 

• Time: 3:30 – 4:30 PM 

• Location: MP3314

• Speaker: Dr. Yongki Lee (Georgia Southern University) 

• Title: Thresholds for traffic flow models with look-ahead dynamics

• Abstract: In this talk, we review various nonlocal traffic flow models with look-ahead interactions. We are interested in the local and global well-posedness of these models. The goal is to understand whether smooth solutions persist in all time, or there is a finite time singularity formation. Such blowup is known as the wave break-down phenomenon, which describes the generation of the traffic jam. We discuss a sharp critical threshold condition on the initial data which distinguishes the global smooth solutions and finite time wave break-down. This is a joint work with Dr. Changhui Tan(University of South Carolina)

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Joint talk with Department Colloquium 

• Date: Thursday, September 12 

• Time: 3:30 – 4:30 PM 

• Location: MP3314

• Speaker: Dr. Shijun Zheng (Georgia Southern University) 

• Title: Singular Beauty of Solitary Waves

• Abstract: I will begin with an introduction of the soliton phenomenon that arises in physics and other branches of natural and applied sciences.  Then I will mainly address the orbital stability problem for such solitons arising in nonlinear quantum media.  In particular, I will elaborate on the rigorous construction of ground state solutions as well as the threshold dynamics for the bi-harmonic NLS and rotating Bose-Einstein condensation. The modeling equation can be derived from Noether’s theorem in mathematical physics. The proof relies on scaling, translation and rotation invariance  that are intrinsic symmetries of the system. Numerical simulations are also presented.