Chris Henderson

The first reaction-diffusion equation developed and studied is the
Fisher-KPP equation.  Introduced in 1937, this population-dynamics model accounts
for the spatial spreading and growth of a species.  Various generalizations of
this model have been studied in the eighty years since its introduction,
including a model with non-local reaction for the cane toads of Australia
introduced by Benichou et. al.  I will begin the talk by giving an extended
introduction on the Fisher-KPP equation and the typical behavior of its
solutions.  Afterwards I will describe the new model for the cane toads equations
and give new results regarding this model.  In particular, I will show how the
model may be viewed as a perturbation of a local equation using a new
Harnack-type inequality and I will discuss the super-linear in time propagation
of the toads.  The talk is based on a joint work with Bouin and Ryzhik.