We propose a local modification of the standard subdiffusion model by introducing the initial Fickian diffusion, which results in a multiscale diffusion model. The developed model resolves the incompatibility between the nonlocal operators in subdiffusion and the local initial conditions and thus eliminates the initial singularity of the solutions of the subdiffusion, while retaining its heavy tail behavior away from the initial time. The well-posedness of the model and high-order regularity estimates of its solutions are analyzed by resolvent estimates, based on which the numerical discretization and analysis are performed. Numerical experiments are carried out to substantiate the theoretical findings.

翻译：本文通过引入初始菲克扩散，对标准次扩散模型进行局部修正，从而构建了一个多尺度扩散模型。该模型解决了次扩散中非局部算子与局部初始条件之间的不兼容性，消除了次扩散解的初始奇异性，同时保留其在远离初始时间后的重尾行为。通过预解估计分析了模型的适定性及其解的高阶正则性估计，并在此基础上进行了数值离散与理论分析。通过数值实验验证了理论结果。