Moving boundary problems

Moving boundary problems on Earth’s surface

In a moving boundary problem one or more of the domain boundaries is an unknown function of time. The classic moving boundary problem, the Stefan problem, is related to the tracking of a sharp liquid/solid front during the melting of ice. A major societal problem of our time is the current rapid rate of degradation of Earth environments and resources through climate change and other anthropogen...

Moving Boundary Problems with Nonlinear Diffusion

Moving boundary problems governed by anomalous diffusion.

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...

On the Weak Solution of Moving Boundary Problems

The weak formulation of moving boundary problems with possibly vanishing specific heat, that is governed by parabolic and/or elliptic differential equations, is developed. The uniqueness of the resulting weak solution is then proved. This approach is used to obtain numerical solutions to some physical examples, which arise in electrochemical machining processes, and in saturated / unsaturated f...

Moving boundary problems and non - uniqueness forthe thin

A variety of mass preserving moving boundary problems for the thin lm equation, u t = ?(u n u xxx) x , are derived (by formal asymptotics) from a number of regularisations, the case in which the substrate is covered by a very thin pre-wetting lm being discussed in most detail. Some of the properties of the solutions selected in this fashion are described and the full range of possible mass pres...