Domain variations and moving boundary problems

Variations of Constrained Domain Functionals Associated with Boundary{value Problems

We study variational formulas for maximizers for domain functionals F (x0; u (x0)), x0 2 , and R F (x; u (x)) dx over all Lipschitz domains satisfying the constraint R g (x) dx = 1. Here u is the solution of a di usion equation in . Functional variations are computed using domain variations which preserve the constraint exactly. We show that any maximizer solves a moving boundary problem for th...

Three-dimensional adaptive domain remeshing, implicit domain meshing, and applications to free and moving boundary problems

Article history: Received 25 March 2013 Received in revised form 30 December 2013 Accepted 6 January 2014 Available online 13 January 2014

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...