Mathematical analysis of a spatially distributed soil carbon dynamics model

Abstract

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.