Speaker: Adrian Lam (Ohio State University)
Title: PDEs in the evolution of dispersal
Abstract: In this talk, we will discuss some recent results in competition model motivated by the evolution of dispersal. This question was first formulated by A. Hastings in 1983 concerning the outcome of competition among species which are identical except for their dispersal strategies. We will also mention the recent progress on the $N$-species model and conjecture Dockery et al. Next, we discuss a structured population model formulated by Perthame & Souganidis which is equivalent to the competition of a continuum of phenotype. For this latter model, we discuss the existence, uniqueness, and stability of equilibrium solutions and their relation to Nash equilibrium, as well as the corresponding time-dependent problem. This is joint work with Steve. Cantrell (Miami), Wenrui Hao (Penn State), Benoit Perthame (Sorbonne) and Yuan Lou (Shanghai Jiaotong).