红楼Y论坛（第六十九讲）-Anisotropic spreading speeds and traveling waves for abstract monotone systems I: asymptotically smooth

红楼Y论坛（第六十九讲）

Topic: Anisotropic spreading speeds and traveling waves for abstract monotone systems I: asymptotically smooth

Time：15:00-16:00  June. 7, 2023(Wednesday）

Place：Room457，Haiqin No.2

Speaker：Jing Chen

Abstract：This paper is devoted to develop the theory of spreading speeds and traveling waves for a class of abstract monotone systems defined on the space of vector-valued functions on canonical group bundle under the asymptotically smooth assumptions along specified directions. Precisely, we develop Weinberger’s dynamical approach in 1982,  and establish the asymptotic annihilation properties for monotone discrete dynamical systems with pointwise asymptotically smooth assumption. Then, we can construct a sequence of lower functions to obtain asymptotic persistence and upward convergence with pointwise asymptotically smooth hypothesis.  In order to obtain the existence of traveling waves for monotone discrete dynamical systems, we make a discrete-continuous orthogonal decomposition of the additive group and propose the pointwise uniformly asymptotically smooth or interval uniformly asymptotically smooth assumption along the "continuous or discrete" direction.