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 $y'(t)=λρ(t)y(t)+b(t)$, $λ<0$ which represents a simplified storage model of the carbon in the soil. In the first part, we show that, for a periodic function $ρ(t)$, 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.

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