两种不同介质被薄膜分隔系统中的反常扩散--吸收过程模型
Model of anomalous diffusion--absorption process in a system consisting of two different media separated by a thin membrane
摘要：
我们提出了一个系统中的扩散-吸收过程的模型，该系统由两个介质由薄的部分渗透膜分隔。在两种介质中，扩散的种类以及过程的参数可能不同。本文从一个简单的粒子在膜系统中随机行走的模型出发，导出了格林函数，并在此基础上求出了膜上的边界条件。边界条件之一是相当复杂的，并采取一个相对简单的形式，在拉普拉斯变换。假设颗粒相互独立地扩散，所得到的边界条件可用于求解描述多层系统中任何初始条件下的过程的微分或微分-积分方程。我们考虑正常的扩散，亚扩散和慢亚扩散过程，我们还建议如何超扩散可以包括在这个模型中。文中给出了用拉普拉斯变换表示的函数，并给出了计算拉普拉斯逆变换的一些实用方法。
英文摘要：
We present the model of a diffusion-absorption process in a system which consists of two media separated by a thin partially permeable membrane. The kind of diffusion as well as the parameters of the process may be different in both media. Based on a simply model of particle's random walk in a membrane system we derive the Green's functions, then we find the boundary conditions at the membrane. One of the boundary conditions are rather complicated and takes a relatively simple form in terms of the Laplace transform. Assuming that particles diffuse independently of one another, the obtained boundary conditions can be used to solve to differential or differential-integral equations describing the processes in multilayered systems for any initial condition. We consider normal diffusion, subdiffusion and slow subdiffusion processes, and we also suggest how superdiffusion could be included in this model. The presented method provides the functions in terms of the Laplace transform and some useful methods of calculation the inverse Laplace transform are shown.
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