7 papers
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…
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…
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…
Curve shortening flow with an ambient force field
Sam Cuthbertson, Glen Wheeler, Valentina-Mira Wheeler
In this paper we consider the anisotropic curve shortening flow in the plane in the presence of an ambient force. We consider force fields in which all their derivatives are bounde…
Existence theory for a bushfire equation
Serena Dipierro, Enrico Valdinoci, Glen Wheeler +1
In a recent paper, we have introduced a new model to describe front propagation in bushfires. This model describes temperature diffusion in view of an ignition process induced by a…
A simple but effective bushfire model: analysis and real-time simulations
Serena Dipierro, Enrico Valdinoci, Glen Wheeler +1
We introduce a simple mathematical model for bushfires accounting for temperature diffusion in the presence of a combustion term which is activated above a given ignition state. Th…