Transport Equation Reduction for a Mathematical Model in Plant Growth

S. Boujena; A. Chiboub; J. Pousin

Mathematical Modelling of Natural Phenomena (2011)

  • Volume: 6, Issue: 2, page 160-172
  • ISSN: 0973-5348

Abstract

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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.

How to cite

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Boujena, S., Chiboub, A., and Pousin, J.. "Transport Equation Reduction for a Mathematical Model in Plant Growth." Mathematical Modelling of Natural Phenomena 6.2 (2011): 160-172. <http://eudml.org/doc/222221>.

@article{Boujena2011,
abstract = {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. },
author = {Boujena, S., Chiboub, A., Pousin, J.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {plant growth; nutrients; hormones; concentration; transport; domain decomposition; asymptotic expansion; MAPDD},
language = {eng},
month = {3},
number = {2},
pages = {160-172},
publisher = {EDP Sciences},
title = {Transport Equation Reduction for a Mathematical Model in Plant Growth},
url = {http://eudml.org/doc/222221},
volume = {6},
year = {2011},
}

TY - JOUR
AU - Boujena, S.
AU - Chiboub, A.
AU - Pousin, J.
TI - Transport Equation Reduction for a Mathematical Model in Plant Growth
JO - Mathematical Modelling of Natural Phenomena
DA - 2011/3//
PB - EDP Sciences
VL - 6
IS - 2
SP - 160
EP - 172
AB - 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.
LA - eng
KW - plant growth; nutrients; hormones; concentration; transport; domain decomposition; asymptotic expansion; MAPDD
UR - http://eudml.org/doc/222221
ER -

References

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  1. O. Besson, J. Pousin. Solution for Linear Conservation Laws with velocity inL∞. Archive for Rational Mechanics and Analysis, 2007.  
  2. S. Boujena , A. Chiboub, J. Pousin. Variational reduction for the transport equation in a multiple branching plant growth model. Congrès International JANO 9 , 9emes journée d’Analyse Numérique et d’Optimisation. Mohammedia, Maroc, 2008.  
  3. S. Boujena, A. Chiboub, J. Pousin. Variational reduction for the transport equation in a multiple branching plant growth model. Mathematical Modelling of Natural Phenomena, 5 (Supplement 2010), No. 7, 11–15.  
  4. N. Bessonov, V. Volpert. Dynamic models of plant growth, Mathematics and mathematical modeling. Publibook, Paris, 2007.  
  5. M. Crouzeix, L. Mignot. Analyse numérique des équations différentielles. Masson, Paris, 1996.  
  6. F. Fontvieille, Décomposition asymptôtique et éléments finis. Thèse de doctorat, université Claude Bernard- Lyon I, 2004.  
  7. F. Fontvieille, G. Panasenko, J. Pousin. FEM implementation for the asymptotic partial decomposition. Applicable Analysis, 86 (2007), No. 5 , 519–536.  
  8. G.P. Panasenko. Multi-scale Modelling for structures and composites. Springer Verlag, 2005.  
  9. G.P. Panasenko. Method of asymptotic partial decomposition of domain. Math. Models and Methods in Appl. Sci., 1 (1998), No. 8, 139–156.  
  10. M. Picq, J. Pousin. Variational reduction for the transport equation and plants growth. In Proccedings of the Conference Modelling of the Heterogeneous Materials with Applications in Constructions and Biological Engineering. Czech Technical University Prague, 2007.  

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