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Applied Mathematics and Computation 218 (2012) 5641-5654
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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

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.
1 :  Mathématiques - Analyse, Probabilités, Modélisation - Orléans (MAPMO)
Université d'Orléans – CNRS : UMR7349
2 :  Department of Mathematics
University of Technical Education of HoChiMinh City
3 :  Department of Mathematics and Computer Science
College of Natural Science, VietNam National University HoChiMinh City
Mathématiques/Equations aux dérivées partielles
Ordinary differential equations – Parabolic differential equations – analytic semi group – T-periodic function – linear drift – Cauchy sequence – series' estimates
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