Geodesic
Transport Equation Reduction for a Mathematical Model in Plant Growth
S. Boujena1 ; A. Chiboub1 ; J. Pousin2
1 Department of Mathematics and computing, Hassan II University, Sciences Faculty, POB 5366 Maarif, Casablanca, Morocco
2 Université de Lyon, INSA de Lyon, ICJ UMR CNRS 5028, 69100 Villeurbanne cedex France
Mathematical modelling of natural phenomena, Tome 6 (2011) no. 2, pp. 160-172.

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In this article a variational reduction method, how to handle the case of heterogenous domains for the Transport equation, is presented. This method allows to get rid of the restrictions on the size of time steps due to the thin parts of the domain. In the thin part of the domain, only a differential problem, with respect to the space variable, is to be approximated numerically. Numerical results are presented with a simple example. The variational reduction method can be extended to thin domains multi-branching in 3 dimensions, which is a work in progress.
DOI : 10.1051/mmnp/20116206

S. Boujena 1 ; A. Chiboub 1 ; J. Pousin 2

1 Department of Mathematics and computing, Hassan II University, Sciences Faculty, POB 5366 Maarif, Casablanca, Morocco
2 Université de Lyon, INSA de Lyon, ICJ UMR CNRS 5028, 69100 Villeurbanne cedex France 
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S. Boujena; A. Chiboub; J. Pousin. Transport Equation Reduction for a Mathematical Model in Plant Growth. Mathematical modelling of natural phenomena, Tome 6 (2011) no. 2, pp. 160-172. doi : 10.1051/mmnp/20116206. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20116206/

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