Nonlinear Dynamics Seminar (Summer 2022, MUN)

Organizer: Drs. Shuwen Xue and Xiaoqiang Zhao

Time and Location: Zoom meeting

Speakers and Abstracts:

1. 9:00am-12:00, May 17, Tuesday, Leyi Jiang (Memorial University), "Propogation dynamics for monotone evolution systems without spatial translation invariance (I)"

2. 9:00am-12:00, May 24, Tuesday, Leyi Jiang (Memorial University), "Propogation dynamics for monotone evolution systems without spatial translation invariance (II)"

3. 9:00am-12:00, May 31, Tuesday, Leyi Jiang (Memorial University), "Propogation dynamics for monotone evolution systems without spatial translation invariance (III)"

4. 10:00am-12:00, June 10, Friday, Tian Hou (Memorial University), "Spreading properties and forced waves for a time-delayed nonlocal equation with a shifting habitat, I. Random diffusion case"

5. 10:00am-12:00, June 17, Friday, Tian Hou (Memorial University), "Spreading properties and forced waves for a time-delayed nonlocal equation with a shifting habitat, II. Nonlocal dispersal case"

6. 10:00am-12:00, June 23, Thursday, Shiliang Wu (XiDian University), "Long time behavior for a periodic Lotka-Volterra reaction-diffusion system with strong competition"

In this talk, we first review some related topics on the the long time behavior of bounded solutions for diffusion equations. Then we consider the the long time behavior of bounded solutions to a two-species time-periodic Lotka-Volterra reaction-diffusion system with strong competition. By transforming the system into a cooperative system on [(0,0),(1,1)], we first show that if the bounded initial value has compact support and equals (1,1) for a sufficiently large x-level, then solutions converge to a pair of diverging periodic traveling fronts. As a by-product, we obtain a sufficient condition for solutions to spread to (1,1). We also prove that if the two species are initially absent from the right half-line x>0 and the slower one dominates the faster one on x<0, then solutions approach a propagating terrace, which means that several invasion speeds can be observed.