论文标题
广义扩散方程与非局部时空：分析和数值分析
Generalized diffusion equation with nonlocality of space-time: analytical and numerical analysis
论文作者
论文摘要
根据非马尔科夫扩散方程，考虑了粒子扩散系数的空间分形和建模 $D^{αα'}(\mathbf{r},\mathbf{r}';t,t')=W(t,t')\bar{D}^{αα'}(\mathbf{r},\mathbf{r}')$ using fractional calculus the generalized Cattaneo--Maxwell--type diffusion equation in已经获得了部分时间和空间衍生物。在恒定扩散系数的情况下，已经进行了分数时间和空间衍生词的Cattaneo--Maxwell扩散方程的频谱的分析和数值研究。随着特征松弛时间的变化，扩散系数和时间$ξ$和空间$α$分形的变化的相位和组速度的数值计算。
Based on the non-Markov diffusion equation taking into account the spatial fractality and modeling for the generalized coefficient of particle diffusion $D^{αα'}(\mathbf{r},\mathbf{r}';t,t')=W(t,t')\bar{D}^{αα'}(\mathbf{r},\mathbf{r}')$ using fractional calculus the generalized Cattaneo--Maxwell--type diffusion equation in fractional time and space derivatives has been obtained. In the case of a constant diffusion coefficient, analytical and numerical studies of the frequency spectrum for the Cattaneo--Maxwell diffusion equation in fractional time and space derivatives have been performed. Numerical calculations of the phase and group velocities with change of values of characteristic relaxation time, diffusion coefficient and indexes of temporal $ξ$ and spatial $α$ fractality have been carried out.
