Large time behavior of differential equations with drifted periodic   coefficients modeling Carbon storage in soil
  This paper is concerned with the linear ODE in the form $y'(t)=\lambda\rho(t)y(t)+b(t)$, $\lambda <0$ which represents a simplified storage model of the carbon in the soil. In the first part, we show that, for a periodic function $\rho(t)$, a linear drift in the coefficient $b(t)$ involves a linear drift for the solution of this ODE. In the second part, we extend the previous results to a classical heat non-homogeneous equation. The connection with an analytic semi-group associated to the ODE equation is considered in the third part. Numerical examples are given. 
Stephane Cordier (MAPMO), Le Xuan Truong, Long Nguyen Thanh, Alain   Pham Ngoc Dinh (MAPMO)