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arXiv · 1505.00678

Analysis of a chemotaxis system modeling ant foraging

Ricardo Alonso·Paulo Amorim·Thierry Goudon
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Abstract

In this paper we analyze a system of PDEs recently introduced in [P. Amorim, {\it Modeling ant foraging: a {chemotaxis} 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 well-posedness 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 \emph{a priori} estimates in Lebesgue spaces.

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Ricardo Alonso, Paulo Amorim, Thierry Goudon. 2015-05-04. Analysis of a chemotaxis system modeling ant foraging. https://arxiv.org/abs/1505.00678

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