Nonlinear Dynamics Seminar (Fall 2025, MUN)

Organizer: Dr. Xiaoqiang Zhao

Time and Location: 9:00pm-11:30pm, Monday, Zoom meeting

Speakers and Abstracts:

1. Sept. 9, Shiheng Fan (Memorial University), "An Impulsive Reaction-Diffusion Model with Asymptotically Periodic Domain" (I)

2. Sept. 16, Shiheng Fan (Memorial University), "An Impulsive Reaction-Diffusion Model with Asymptotically Periodic Domain" (II)

3. Sept. 23, Yequan Liang(Memorial University), "Global dynamics of a mosquito growth model with a periodic delay and pair formation" (I)

4. Sept. 29, Yequan Liang(Memorial University), "Global dynamics of a mosquito growth model with a periodic delay and pair formation" (II)

5. Oct. 6, Tianran Zhang (Memorial University), "Traveling wave solutions to a nonlocal diffusion SEIR epidemic model with bilinear incidence"

In this talk, I will discuss the existence of traveling wave solutions for a nonlocal diffusion SEIR epidemic model with bilinear incidence rates, and present necessary and sufficient conditions for the existence of such solutions. The key to the problem lies in proving the boundedness of the traveling wave solutions. Previous discussions on the boundedness of traveling wave solutions in nonlocal diffusion models (such as predator-prey models) involved studying solutions of single linear nonlocal diffusion equations and analyzing the monotonicity of traveling waves. However, due to the higher dimensionality of our model, the methods previously applied to predator-prey models are not easily adaptable here. We will introduce the Laplace transform to establish the boundedness of the traveling wave solutions, thereby avoiding detailed discussions on the subtle properties of the waves. Only the unboundedness of the solutions is required to derive a contradiction.

6. Oct. 20, Junfeng He (Shenzhen Technology University), "Asymptotic propagation speeds of the Fisher-KPP equation with an effective boundary condition on a road"

Of concern here is the Fisher-KPP equation on the x and y plane with an "effective boundary condition" imposed on the x-axis. This model, recently derived by H. Li and the third author (Li and Wang in Nonlinearity 30: 3853-3894, 2017), is meant to model the scenario of fast diffusion on a "road" in a large "field". In Li and Wang (2017), the asymptotic propagation speed of this model in the horizontal direction is obtained, showing that the fast diffusion on the road does enhance spreading speed in that direction in the field. In this paper, we study the propagation speeds in all directions, showing that away from the x-axis by a certain angle (which can be explicitly calculated in terms of parameters), the fast diffusion on the road increases propagation speeds, with the speed getting larger when the direction is closer to the x-axis. We also obtain the asymptotic spreading shape for the model. These results are parallel to the ones obtained by Berestycki et al. (Commun. Math. Phys. 343, 207-232, 2016) for a different model which is meant to model the same physical phenomenon.