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arXiv · 2007.03770

Propagation Dynamics for Monotone Evolution Systems without Spatial Translation Invariance

Taishan Yi·Xiao-Qiang Zhao
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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.

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Taishan Yi, Xiao-Qiang Zhao. 2020-07-07. Propagation Dynamics for Monotone Evolution Systems without Spatial Translation Invariance. https://arxiv.org/abs/2007.03770

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