Andrej Zlatos proposed that we look at a 1-dimensional PDE which models heating. The PDE itself is cross between KPP reaction-diffusion equations and Ignition reaction diffusion equations. Ignition reaction diffusion equations are great for modelling heating of materials such as wood, because wood heats until a certain threshold and then it ignites. On the other hand KPP is better for modelling materials such as metal, which heats in a more steady fashion. Our PDE may model something which is wood in certain patches and metal in other patches. We prove conditions for existence and non-existence of a travelling front. Travelling fronts are kind of like “heat waves” and this is a standard thing to check for with reaction-diffusion PDEs. I think of what we did as a kind of “barrier-method” proof since we deal with constructing super-solution and sub-solution bounds.
- Andrej Zlatos (Adviser)
- Cole Graham (Undergraduate)
- Tau Shean Lim (Graduate student)
- David Weber (Undergraduate)
- Please see our paper on Arxiv and (hopefully) in the Journal “Nonlinearity”
- We also won a small undergraduate award for this project:
Note to self: I can add links to my collaborator’s professional pages later