Analysis of a chemotaxis system modeling ant foraging
Abstract
In this paper we analyze a system of PDEs recently introduced in
[P. Amorim, Modeling ant foraging: a PDE approach with pheromones
and trail formation], in order to describe the dynamics of ant foraging.
The system is made of convection-diffusion-reaction equations, and the
coupling is driven by chemotaxis mechanisms. We establish the wellposedness
for the model, and investigate the regularity issue for a large
class of integrable data. Our main focus is on the (physically relevant)
two-dimensional case with boundary conditions, where we prove that the
solutions remain bounded for all times. The proof involves a series of fine
a priori estimates in Lebesgue spaces