Large time behavior of differential equations with drifted periodic coefficients modeling Carbon storage in soil

Stephane Cordier (1) , Le Xuan Truong (2) , Long Nguyen Thanh (3) , Alain Pham Ngoc Dinh (1)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
2 Department of Mathematics
3 Department of Mathematics and Computer Science

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.

Mots clés: Ordinary differential equations; Parabolic differential equations; analytic semi group; T-periodic function; linear drift; Cauchy sequence; series' estimates

Domaines: Equations aux dérivées partielles [math.AP]

Stephane Cordier, Le Xuan Truong, Long Nguyen Thanh, Alain Pham Ngoc Dinh. Large time behavior of differential equations with drifted periodic coefficients modeling Carbon storage in soil. Applied Mathematics and Computation, 2012, 218, pp.5641-5654. ⟨hal-00323332v2⟩