Title: Dirac concentration in a integro-PDE model from adaptation
Speaker: Adrian Lam (Ohio State University)
Abstract: We consider a mutation-selection model of a population structured by the spatial variables and a trait variable which is the diffusion rate. Competition for resource is local in spatial variables, but nonlocal in the trait variable. We establish the existence and asymptotic profile of a steady state solution. 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. Similar result was independently obtained by B. Perthame and T. Souganidis via an elegant method. I will present a sketch of proof blending the arguments of both papers. This is joint work with Yuan Lou and Wenrui Hao (Penn State).
Seminar URL: https://research.math.osu.edu/pde/