title: Moving boundary problems governed by anomalous diffusion.
abstract: Anomalous diffusion can be characterized by a mean-squared displacement 〈x(2)(t)〉 that is proportional to t(α) where 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.
authors.affiliation: Department of Engineering Sciences and Applied Mathematics ,  Northwestern University ,  2145 Sheridan Road, Evanston, IL 60208-3125, USA.
authors.forename: Christopher J
authors.initials: CJ
authors.lastname: Vogl
authors.forename: Michael J
authors.initials: MJ
authors.lastname: Miksis
authors.forename: Stephen H
authors.initials: SH
authors.lastname: Davis