دانلود رایگان مقاله انگلیسی تجزیه و تحلیل ریاضی مدل دینامیک کربن خاک از نوع کموتاکسی - اشپرینگر 2018

Abstract

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.

5 A Three Dimensional Domain

In order to prove the global existence of a solution of system (Ph), we supposed in the previous sections that Ω was a two dimensional domain and the initial conditions (u0, v0) ∈ L∞(Ω)×H1+ε0 (Ω) were nonnegative and verifying some regularity conditions. These conditions are quite restrictive for a model of soil organic carbon and three dimensional domains are obviously more relevant in applications than bidimensional ones. In this section we prove that if Ω is of dimension less than or equal to 3, if h = eh (4.1) and if both initial conditions and forcing term are nonnegative and less regular that in the previous section: (u0, v0) ∈ (L 2 (Ω))2 and f ∈ L 2 (0, T ;L 2 (Ω)), then the system (Ph) has a global nonnegative solution. Furthermore, if (u0, v0) ∈ (L∞(Ω))2 and f ∈ L∞(ΩT ), then the solution is unique.