Title: Spreading properties and forced traveling waves of reaction-diffusion equations in a time-heterogeneous shifting environment
Speaker: Lei Zhang (Harbin Institute of Technology，Weihai)
Time: September 9th, 2022
Place: Online
Abstract: In this talk, I will report our recent research on the propagation dynamics of a large class of nonautonomous reaction-diffusion equations with the time-dependent shifting speed having a uniform mean c. Under the assumption that in two directions of the spatial variable there are two limiting equations with one admitting a spreading speed c* and the other being asymptotic to annihilation, we show that the solutions with compactly supported initial data go to zero eventually when c is less than or equal to -c*, the leftward spreading speed is -c* when c is greater than -c*, and the rightward spreading speed is c and c* when c is in the interval (-c*,c*) and c is greater than or equal to c*, respectively. We also establish the existence, uniqueness and nonexistence of the forced traveling wave in terms of the sign of c-c*. This talk is based on a joint work with Prof. Xiao-Qiang Zhao.
Title: Dynamics of Nonlocal Dispersal Competition Systems in Shifting Habitats
Speaker: Jiabing Wang (China University of Geosciences，Wuhan)
Time: September 9th, 2022
Place: Online
Abstract: Climate changes caused by global warming, industrialization and overdevelopment have led to the shifting of habitats for biological species and seriously threatened and destroyed the ecological environment and biological diversity. It is very important to study the the effects of the climate change on competitive outcomes between species. In this talk, I will report our recent results on the asymptotic propagations and multi-type forced wave solutions for nonlocal dispersal competition systems in (time-periodic) shifting habitats.
Title: Long-time asymptotics of 3-D axisymmetric Navier-Stokes equations in critical spaces
Speaker: Yanlin Liu (Beijing Normal University)
Time: June 3rd, 2021 13:50-14:50
Place: Room 108, Zhiyuan Buildinig
Abstract: We show that any unique global solution (here we do not require any smallness condition beforehand) to 3-D axisymmetric Navier-Stokes equations in some scaling invariant spaces must eventually become a small solution. In particular, we show that the limits of $\|\omega^\theta(t)/r\|_{L^1}$ and $\|u^\theta(t)/\sqrt r\|_{L^2}$ are all $0$ as $t$ tends to infinity. And by using this, we can refine some decay estimates for the axisymmetric solutions.