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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.

Keywords

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}
}
R2 v1 2026-06-23T16:56:03.039Z