Andrew Hale

We use partial differential equations to model various phenomena, including flame propagation, tumor growth, and ice in the polar seas. Despite the fact that the models are widely used, the models sometimes yield non-physical results. This research project focuses on thin one-phase models, which are used to study flame propagation. The problem we are trying to address is that the model sometimes does not yield unique solutions. We want to show a generic uniqueness result, which states that under normal, physical conditions, a unique solution is obtained.