The paper was completed during the Summer 2004 REU program at Tulane University.
The theme of the applied math program was the effect of diffusion on the solutions of reaction-diffusion equations. During the program, Xuefeng Wang (Tulane University) taught a crash course in PDE's, and Wei-Ming Ni (University of Minnesota) delivered a series of lectures on reaction-diffusion systems.
Thereafter, my group worked with John Alford (Tulane University) studying the solutions of reaction-diffusion equations. We found numerical evidence suggesting the existence of non-constant stable steady-state solutions to a reaction-diffusion equation in two types of star-shaped domains. In addition, we numerically analyzed the relationship between the diffusion constant, the aperture width, and the nature of the steady-state.
John Alford, VIGRE Postdoctoral Fellow, Mathematics Department,Tulane University