%0 Journal Article
%9 ACL : Articles dans des revues avec comité de lecture répertoriées par l'AERES
%A Hammoudi, A.
%A Iosifescu, O.
%A Bernoux, Martial
%T Mathematical analysis of a spatially distributed soil carbon dynamics model
%D 2017
%L PAR00016507
%G ENG
%J Analysis and Applications
%@ 0219-5305
%K Soil organic carbon dynamics ; reaction-diffusion-advection system ; positive weak solutions ; periodic weak solutions
%M ISI:000407148600001
%N 6
%P 771-793
%R 10.1142/s0219530516500081
%U https://www.documentation.ird.fr/hor/PAR00016507
%V 15
%W Horizon (IRD)
%X The aim of this paper is to study the mathematical properties of a new model of soil carbon dynamics which is a reaction-diffusion-advection system with a quadratic reaction term. This is a spatial version of Modeling Organic changes by Micro-Organisms of Soil model, recently introduced by M. Pansu and his group. We show here that for any nonnegative initial condition, there exists a unique nonnegative weak solution. Moreover, if we assume time periodicity of model entries, taking into account seasonal effects, we prove existence of a minimal and a maximal periodic weak solution. In a particular case, these two solutions coincide and they become a global attractor of any bounded solution of the periodic system.
%$ 068 ; 020