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Large time behavior of differential equations with drifted periodic coefficients modeling Carbon storage in soil
Cordier S., Xuan Truong L., Nguyen Thanh L., Pham Ngoc Dinh A.
Applied Mathematics and Computation 218 (2012) 5641-5654 - http://hal.archives-ouvertes.fr/hal-00323332
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Mathématiques/Equations aux dérivées partielles
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 :  Mathématiques - Analyse, Probabilités, Modélisation - Orléans (MAPMO)
Université d'Orléans – CNRS : UMR7349
Fédération Denis Poisson, Bâtiment de Mathématiques, B.P. 6759, 45067 Orléans cedex 2
2 :  Department of Mathematics
University of Technical Education of HoChiMinh City
01 Vo Van Ngan Str., Thu Duc Dist HoChiMinh City, Vietnam
Viet Nam
3 :  Department of Mathematics and Computer Science
College of Natural Science, VietNam National University HoChiMinh City
227 Nguyen Van Cu Str., Dist. 5, HoChiMinh City, Vietnam
Viet Nam
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.

Applied Mathematics and Computation
Publisher Elsevier
ISSN 0096-3003 

Ordinary differential equations – Parabolic differential equations – analytic semi group – T-periodic function – linear drift – Cauchy sequence – series' estimates
34E05, 35K, 40A05
18 pages

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