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

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

2008-09-20

arxiv.org/abs/0809.3530v2

Applied Mathematics and Computation 218 (2012) 5641-5654

Mathematics

Analysis of PDEs

18 pages

Scientific paper

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.

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