Analysis of a chemotaxis system modeling ant foraging

作者：Alonso Ricardo; Amorim Paulo; Goudon Thierry^*

来源：Mathematical Models and Methods in Applied Sciences, 2016, 26(9): 1785-1824.

DOI：10.1142/S0218202516500457

• Ant foraging
• chemotaxis
• animal movement
• reaction-diffusion equations
• De Giorgi's method

In this paper, we analyze a system of PDEs recently introduced in [P. Amorim, Modeling ant foraging: A chemotaxis approach with pheromones and trail formation, J. Theor. Biol. 385 (2015) 160-173], 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 focus is on the (physically relevant) two-dimensional case with boundary conditions, where we prove that the solutions remain bounded for all times. Further, we prove a hypercontractivity result (instantaneous formation of all L-p-norms, p is an element of (1,+infinity]). The proofs involve a series of fine a priori estimates in Lebesgue spaces and a De Giorgi level set technique.

• 出版日期2016-8
• 单位INRIA