7 papers
Concentration-compactness for the geometric polyharmonic heat flow
James McCoy, Scott Parkins, Glen Wheeler +1
We develop a concentration-compactness theory for geometric evolution equations of arbitrarily high order, using the geometric polyharmonic heat flow of closed immersed surfaces in…
Homogeneous Sobolev gradient flow of the length functional
Philip Schrader, Glen Wheeler, Valentina Wheeler
The well-known curve shortening flow can be formulated as the gradient flow of the length functional on the space of immersed closed planar curves, where the gradient is taken with…
On the basin of attraction for the free boundary free elastic flow
Klaus Deckelnick, Hans-Christoph Grunau, Robert Nürnberg +2
The free boundary free elastic flow is the steepest descent gradient flow for the elastic energy of curves meeting parallel lines perpendicularly. In this article we prove that the…
Bushfires and Balance: Proactive versus Reactive Policies in Prescribed Burning
Serena Dipierro, Enrico Valdinoci, Glen Wheeler +1
We introduce a new mathematical model to explore the dynamic relationship between prescribed burning and bushfire occurrence, formulated as a system of ordinary differential equati…
A curvature flow approach to dorsal closure modelling
Shuhui He, Ben Whale, Glen Wheeler +1
In this paper we propose and study a curvature-based mathematical model for dorsal closure in embryonic drosophila. Using an analysis that mixes maximum-principle and integral-esti…
Self-sustaining traveling fronts for a model related to bushfires
Serena Dipierro, Enrico Valdinoci, Glen Wheeler +1
This article investigates a mathematical model for bushfire propagation, focusing on the existence and properties of translating solutions. We obtain quantitative bounds on the env…