Georgia Institute of Technology College of Sciences

The talk focuses on positive equilibrium (i.e. time-independent)solutionsto mathematical models for the dynamics of populations structured by ageand spatial position. This leads to the study of quasilinear parabolicequations with nonlocal and possibly nonlinear initial conditions. Weshallsee in an abstract functional analytic framework how bifurcationtechniquesmay be combined with optimal parabolic regularity theory to establishtheexistence of positive solutions. As an application of these results wegivea description of the geometry of coexistence states in a two-parameterpredator-prey model.