论文标题
常规和不规则扩散方程的高级自相似解决方案
Advanced self-similar solutions of regular and irregular diffusion equations
论文作者
论文摘要
我们研究了变量的适当更改的扩散方程。该方程通常是部分微分方程（PDE）。使用自相似和相关的Ansatätze，我们将扩散的PDE转换为普通的微分方程。 PDE的解决方案属于适用于无限视野的功能家族。在演讲中，我们强调了身体上合理的解决方案。我们还研究了依赖时间的扩散现象，其中扩散可能会随着时间而变化。为了描述我们考虑时间依赖性扩散系数的过程。所获得的分析解决方案都可以用Kummer或Whittaker型功能表达。
We study the diffusion equation with an appropriate change of variables. This equation is in general a partial differential equation (PDE). With the self-similar and related Ansatätze we transform the PDE of diffusion to an ordinary differential equation. The solutions of the PDE belong to a family of functions which are presented for the case of infinite horizon. In the presentation we accentuate the physically reasonable solutions. We also study time dependent diffusion phenomena, where the spreading may vary in time. To describe the process we consider time dependent diffusion coefficients. The obtained analytic solutions all can be expressed with Kummer's or Whittaker-type of functions.
