In the following we will discuss some known results on the behavior of solutions to reaction-diffusion equations. We will be concerned with the stability of steady-state solutions in different classes of domains. A result in Matano states that for convex domains, every non-constant stable steady-state solution to the reaction-diffusion equation is unstable. As an application of a theorem in Matano, we show that this result for convex domains does not generalize to the larger class of star-shaped domains.
John Alford, VIGRE Postdoctoral Fellow, Mathematics Department,Tulane University email@example.com
"Non-Constant Stable Solutions to Reaction-Diffusion Equations in Star-Shaped Domains,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 6
, Article 4.
Available at: https://scholar.rose-hulman.edu/rhumj/vol6/iss2/4