Moving boundary problems governed by anomalous diffusion

作者：Vogl Christopher J^*; Miksis Michael J; Davis Stephen H

来源：Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences, 2012, 468(2147): 3348-3369.

DOI：10.1098/rspa.2012.0170

• moving boundary
• anomalous diffusion
• subdiffusion
• fractional diffusion equation

Anomalous diffusion can be characterized by a mean-squared displacement < x(2)(t)> that is proportional to t(alpha) where alpha not equal 1. A class of one-dimensional moving boundary problems is investigated that involves one or more regions governed by anomalous diffusion, specifically subdiffusion (alpha < 1). A novel numerical method is developed to handle the moving interface as well as the singular history kernel of subdiffusion. Two moving boundary problems are solved: the first involves a subdiffusion region to the one side of an interface and a classical diffusion region to the other. The interface will display non-monotone behaviour. The subdiffusion region will always initially advance until a given time, after which it will always recede. The second problem involves subdiffusion regions to both sides of an interface. The interface here also reverses direction after a given time, with the more subdiffusive region initially advancing and then receding.

• 出版日期2012-11-8
• 单位西北大学