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Propagation dynamics for monotone evolution systems without spatial translation invariance. (English) Zbl 1446.35032

Summary: 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.

MSC:

35C07 Traveling wave solutions
35B40 Asymptotic behavior of solutions to PDEs
37C65 Monotone flows as dynamical systems
37L15 Stability problems for infinite-dimensional dissipative dynamical systems
92D25 Population dynamics (general)
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