Moving boundary problems governed by anomalous diffusion

Christopher J. Vogl*, Michael J. Miksis, Stephen H. Davis

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

Anomalous diffusion can be characterized by a mean-squared displacement 〈x2(t)〉 that is proportional tα ta where a α = 1. A class of one-dimensional moving boundary problems is investigated that involves one or more regions governed by anomalous diffusion, specifically subdiffusion (α < 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.

Original languageEnglish (US)
Pages (from-to)3348-3369
Number of pages22
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume468
Issue number2147
DOIs
StatePublished - Nov 8 2012

Keywords

  • Anomalous diffusion
  • Fractional diffusion equation
  • Moving boundary
  • Subdiffusion

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)

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