Invited by Prof.Zhicheng Wang and Associate Prof. Liang Zhang, Associate Prof. Weiwei Ding from South China Normal University will give a lecture online.

Title: Admissible speeds in spatially periodic bistable reaction-diffusion equations

Time: 9:00 a.m.,Apr. 27th, 2021

Conference ID: 219 169 763( Tencent Conference)

Abstract: Spatially periodic reaction-diffusion equations typically admit pulsating waves whichdescribe the transition from one steady state to another. Due to the heterogeneity, ingeneral such an equation is not invariant by rotation and therefore the speed of thepulsating wave may a priori depend on its direction. However, little is actually knownin the literature about whether it truly does: surprisingly, it is even known in theone-dimensional monostable Fisher-KPP case that the speed is the same in the opposite directions despite the lack of symmetry. In this talk,we will discuss this issue in thebistable case and show that the set of admissible speeds is actually rather large, whichmeans that the shape of propagation may indeed be asymmetrical. More precisely, weshow in any spatial dimension that one can choose an arbitrary large number of directions, and find a spatially periodic bistable type equation to achieve any combinationof speeds in those directions, provided those speeds have the same sign. In particular,in spatial dimension 1 and unlike the Fisher-KPP case, any pair of (either nonnegativeor nonpositive) rightward and leftward wave speeds is admissible.