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ABSTRACT In this paper, we first study the propagation dynamics of a nonlocal diffusion equation in which the diffusion coefficient depends on a shifting environment. More precisely, we investigate the spreading speed of a Fisher‐KPP equation with nonlocal diffusion and compactly supported initial datum, in the presence of a monotone shifting diffusion coefficient driven by a given forcing speed. By constructing super‐ and sub‐solutions and applying the comparison principle, we establish the asymptotic spreading behavior of the solution. Furthermore, we explore the existence and nonexistence of traveling fronts in the case where the diffusion coefficient is nonincreasing.
Zhao et al. (Fri,) studied this question.
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