Abstract: We consider an integro-PDE model for a population structured by the spatial variables and a trait variable which is the diffusion rate. We focus on the asymptotic profile of positive steady state solutions. Our result shows that in the limit of small mutation rate, the solution remains regular in the spatial variables and yet concentrates in the trait variable and forms a Dirac mass supported at the lowest diffusion rate. This talk is based on joint work with Professor King-Yeung Lam, Ohio State University.
