This paper is concerned with the asymptotic behavior of the solutions for Nicholson's blowflies equation with nonlocal dispersion subjected to Dirichlet boundary condition. We first prove the existence and uniqueness of the solution for the initial boundary value problem and its non-trivial steady state. Then we give a threshold result on global stability of equilibria: when $D{\lambda }_1+\delta >p$, the solution time-exponentially converges to the constant equilibrium 0 for any large initial data; when $D{\lambda }_1+\delta <p$, the solution time-asymptotically converges to its positive steady-state $\varphi (x)$ for any large initial data, once $1<\frac{p}{\delta }\le e$, where D>0 is the diffusion coefficient, $\delta >0$ is the death rate, p>0 is the birth rate and ${\lambda }_1>0$ is the principal eigenvalue for the nonlocal characteristic equation. The adopted approach is the energy method and the monotonic technique.

本文关注在 Dirichlet 边界条件下具有非局部色散的 Nicholson 的苍蝇方程解的渐近行为。我们首先证明了初始边值问题及其非平凡稳态解的存在性和唯一性。然后我们给出均衡全局稳定性的阈值结果：当$D{\lambda }_1+\delta >p$，对于任何大的初始数据，解时间指数收敛到恒定平衡 0；什么时候$D{\lambda }_1+\delta <p$, 解时间渐近收敛到其正稳态$\phi (X)$对于任何大的初始数据，一次$1<\frac{p}{\delta }\le e$，其中D >0 是扩散系数，$\delta >0$是死亡率，p >0 是出生率，${\lambda }_1>0$是非局部特征方程的主特征值。采用的方法是能量法和单调法。