Propagation dynamics of a reaction-diffusion equation in a time-periodic shifting environment

2020/04/19 by Fang, Jian, Peng, Rui, Zhao, Xiao-Qiang · 2 citations
#35B40 #35C07 #35K57 #92D25 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2004.08766

Abstract

This paper concerns the nonautonomous reaction-diffusion equation u_t=u_xx+ug(t,x-ct,u), tgt;0,x∈ℝ, where c∈ℝ is the shifting speed, and the time periodic nonlinearity ug(t,ξ,u) is asymptotically of KPP type as ξ→-∞ and is negative as ξ→+∞. Under a subhomogeneity condition, we show that there is c^*>0 such that a unique forced time periodic wave exists if and only |c|< c^* and it attracts other solutions in a certain sense according to the tail behavior of initial values. In the case where |c|≥ c^*, the propagation dynamics resembles that of the limiting system as ξ→± ∞, depending on the shifting direction.

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• Spatio-temporal dynamics for a class of monotone evolution systems
• Invasion Fronts in Shifting Habitats and Competition Systems: A Hamilton-Jacobi Approach and Nonlocal Effects

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