Mathematical Analysis of a Chemotaxis-Type Model of Soil Carbon Dynamic

The goal of this paper is to study the mathematical properties of a new model of soil carbon dynamics which is a reaction-diffusion system with a chemotactic term, with the aim to account for the formation of soil aggregations in the bacterial and microorganism spatial organization(hot spot in soil). This is a spatial and chemotactic version of MOMOS(Modelling Organic changes by Micro-Organisms of Soil), a model recently introduced by M. Pansu and his group. The authors present here two forms of chemotactic terms, first a"classical" one and second a function which prevents the overcrowding of microorganisms.They prove in each case the existence of a nonnegative global solution, and investigate its uniqueness and the existence of a global attractor for all the solutions.