Propagation Dynamics for Monotone Evolution Systems without Spatial Translation Invariance
Analysis of PDEs
2020-07-09 v1
Abstract
In this paper,under an abstract setting we establish the existence of spatially inhomogeneous steady states and the asymptotic propagation properties for a large class of monotone evolution systems without spatial translation invariance. Then we apply the developed theory to study traveling waves and spatio-temporal propagation patterns for time-delayed nonlocal equations, reaction-diffusion equations in a cylinder, and asymptotically homogeneous KPP-type equations. We also obtain the existence of steady state solutions and asymptotic spreading properties of solutions for a time-delayed reaction-diffusion equation subject to the Dirichlet boundary condition.
Cite
@article{arxiv.2007.03770,
title = {Propagation Dynamics for Monotone Evolution Systems without Spatial Translation Invariance},
author = {Taishan Yi and Xiao-Qiang Zhao},
journal= {arXiv preprint arXiv:2007.03770},
year = {2020}
}