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Existence and Stability of Random Transition Waves for Nonautonomous Fisher-KPP Equations with Nonlocal Diffusion (2305.19762v1)
Published 31 May 2023 in math.AP and math.DS
Abstract: In this paper, we study the existence and stability of random transition waves for time heterogeneous Fisher-KPP Equations with nonlocal diffusion. More specifically, we consider general time heterogeneities both for the nonlocal diffusion kernel and the reaction term. We use the comparison principle of the scalar equation and the method of upper and lower solutions to investigate the existence of random transition wave solution when the wave speed is large enough. In addition, we show the stability of random transition fronts for non-autonomous Fisher-KPP equations with nonlocal diffusion.