In this paper we study the approximation of random diffusion by nonlocal diffusion with properly rescaled kernels in age-structured models. First we show that solutions of age-structured models with nonlocal diffusion under Dirichlet and Neumann boundary conditions converge to solutions of the corresponding age-structured models with random diffusion under Dirichlet and Neumann boundary conditions, respectively. Then we prove that the principal eigenvalues of the nonlocal operators in age-structured models under Dirichlet and Neumann boundary conditions converge to the principal eigenvalues of the corresponding Laplace operators in age-structured models under Dirichlet and Neumann boundary conditions, respectively.

在本文中，我们研究了年龄结构模型中具有适当比例缩放的内核的非局部扩散与随机扩散的近似。首先，我们证明了在Dirichlet和Neumann边界条件下具有非局部扩散的年龄结构模型的解分别收敛于在Dirichlet和Neumann边界条件下具有随机扩散的相应年龄结构模型的解。然后我们证明了在Dirichlet和Neumann边界条件下年龄结构模型中非局部算子的主要特征值分别收敛于在Dirichlet和Neumann边界条件下年龄结构模型中相应的Laplace算子的主要特征值。