## Front slowdown due to non-local interactions

- April 11, 2019
- 3 p.m.
- LeConte 317R

## Abstract

Reaction-diffusion equations taking into account non-local competition have gathered substantial interest in recent years. Incorporating such non-local interactions allows to model a richer class of phenomena; however, major technical difficulties arise, such as the absence of a maximum principle. Despite this, early results seemed to suggest that the speed of propagation was unaffected by these non-local terms, that is, the front of the non-local equation has the same shape and speed as that of its local analogue. In this talk we develop an understanding of the reason for this, and then show that it need not always hold. Indeed, we discuss a model arising naturally in ecology (the cane toads equation) for which long-range non-local interactions slow down the front. To prove this, we develop a new characterization of the front via a variational problem coming from a family of Hamilton-Jacobi equations that we then study in-depth.