Mathematical analysis of a chemotaxis-type model of soil carbon dynamic.

Alaaeddine Hammoudi (1) , Oana Iosifescu (1)

1 IMAG - Institut Montpelliérain Alexander Grothendieck

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 MicroOrganisms of Soil), a model recently introduced by M. Pansu and his group. We present here two forms of chemotactic terms, first a " classical " one and second a function which prevents the overcrowding of microorganisms. We prove in each case the existence of a nonnegative global solution, we investigate its uniqueness and the existence of a global attractor for all the solutions.

Mots clés: Soil organic carbon dynamics; reaction-diffusion-advection; system; positive weak solutions; periodic weak solutions

Domaines: Equations aux dérivées partielles [math.AP]

Alaaeddine Hammoudi, Oana Iosifescu. Mathematical analysis of a chemotaxis-type model of soil carbon dynamic.. Chinese Annals of Mathematics - Series B, 2018, 39 (2), pp.253-280. ⟨10.1007/s11401-018-1063-7⟩. ⟨hal-01818727⟩