Le mardi 20 octobre 2015 à 17h00 - Salle 9.11
Alaaeddine HammoudiWe are interested here in modelling the carbon cycle in soil. In the first part we study a non linear system of ordinary differential equations [1]. We will analyze this model and prove the existence and uniqueness of a positive solution, using the theory of cooperative differential systems due to Smith [2]. A more recent model takes into account the space dependence of the carbon cycle. Thus, the model becomes a reaction-diffusion-advection non linear PDE system. We will show in this part that this second model admits also a unique positive weak solution for reasonable hypothesis of the data. In order to study the effect of chemotaxis on the phenomena we derived two simple models and we showed the capability of the model to produce patterns under suitable conditions. We will explain [3] why considering only diffusion does not provide spatial self-organization of the microbes, as observed by Vogel [4] Finally, we derived a continuous-quality model derived from MOMOS and using the methodology of Agren, Bosatta [5]. The model was calibrated and validated using data collected by Pansu. - [1] Pansu et al, Modeling organic transformations by microorganisms of soils in six contrasting ecosystems: validation of the MOMOS model. Global Biogeochem. Cycles, 2010. [2] H. L. Smith, Monotone Dynamical Systems, An introduction to the theory of competitive and cooperative systems, Amer. Math. Soc, 1995. [3] J.D. Murray, Mathematical Biology, Vol. II, Springer, 2003. [4] Vogel et al, Submicron structures provide preferential spotsfor carbon and nitrogen sequestration in soils}, Nature communications, 2014. [5] Bosatta et al, Dynamics of Carbon and Nitrogen in the Organic Matter of the Soil: A Generic Theory, The American Naturalist, 2014.