Abstract This paper investigates the dynamics of a general reaction-diffusion-advection equation with nonlocal delay effect and Dirichlet boundary condition. The existence and stability of positive spatially nonhomogeneous steady state solution are shown. By analyzing the distribution of eigenvalues of the infinitesimal generator associated with the linearized equation, the existence of Hopf bifurcation is proved. We introduce the weighted space to overcome the hurdle from advection term. We also show that the effect of adding a term advection along environmental gradients to Hopf bifurcation values for a Logistic equation with nonlocal delay.

中文翻译：

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具有非局部延迟效应的反应-扩散-平流方程中的 Hopf 分岔

摘要 本文研究了具有非局部延迟效应和狄利克雷边界条件的一般反应-扩散-平流方程的动力学。显示了正空间非均匀稳态解的存在性和稳定性。通过分析与线性化方程相关的无穷小发生器的特征值分布，证明了Hopf分岔的存在。我们引入了加权空间来克服平流项的障碍。我们还展示了沿环境梯度向具有非局部延迟的 Logistic 方程的 Hopf 分岔值添加术语平流的效果。