Elaine Crooks (Swansea University):

Title: Highly nonlinear large-competition limits of elliptic systems

Abstract:

In this talk, I will discuss the effect of different types of competitive interaction terms on the large-interaction limit of nonlinear elliptic systems modelling the steady states of populations that compete in some region. As the competition rate tends to infinity, non-negative solutions of quite simple-looking systems converge to the positive and negative parts of solutions of a scalar limit problem which may be much more strongly nonlinear than the original system, possibly with quadratic growth in the gradient of the limit function. This is joint work with Norman Dancer.