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.

中文翻译：

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无空间平移不变性的单调演化系统的传播动力学

摘要 本文在一个抽象的背景下，我们建立了一大类没有空间平移不变性的单调演化系统的空间非均匀稳态的存在性和渐近传播特性。然后，我们应用开发的理论来研究时滞非局部方程、圆柱反应扩散方程和渐近齐次 KPP 型方程的行波和时空传播模式。我们还获得了服从狄利克雷边界条件的时滞反应扩散方程的稳态解的存在性和解的渐近扩展特性。