We establish that , the solution of a nonlocal diffusion model with a weakly singular kernel converges asymptotically to the solution of the corresponding Fickian diffusion equation. The diffusion tensor of the Fickian equation is determined by half of the covariance matrix, with serving as the probability density function. Numerical experiments are performed to validate our findings. Additionally, we observe that the mean square displacement of the nonlocal diffusion model exhibits a linear relationship with respect to time .

中文翻译：

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弱奇异核非局部扩散模型分析

我们确定，具有弱奇异核的非局部扩散模型的解渐近收敛于相应的 Fickian 扩散方程的解。 Fickian方程的扩散张量由协方差矩阵的一半决定，并作为概率密度函数。进行数值实验来验证我们的发现。此外，我们观察到非局部扩散模型的均方位移与时间呈线性关系。