Variational Reduction for the Transport Equation in a Multiple Branching Plants Growth Model

S. Boujena; A. Chiboub; J. Pousin

Mathematical Modelling of Natural Phenomena (2010)

  • Volume: 5, Issue: 7, page 11-15
  • ISSN: 0973-5348

Abstract

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Plant growth depends essentially on nutrients coming from the roots and metabolites produced by the plant. Appearance of new branches is determined by concentrations of certain plant hormones. The most important of them are Auxin and Cytokinin. Auxin is produced in the growing, Cytokinin in either roots or in growing parts. Many dynamical models of this phenomena have been studied in [1]. In [5], the authors deal with one branch model. In this work, we focus our interest on a multiple branch model. We deal with the transport equation in domains of different sizes. A variational reduction type method [3] based on asymptotic partial decomposition introduced in [2] (see also [4]) is used. In this work we consider the transport equation in decomposed domain with a general right hand side

How to cite

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Boujena, S., Chiboub, A., and Pousin, J.. Taik, A., ed. "Variational Reduction for the Transport Equation in a Multiple Branching Plants Growth Model." Mathematical Modelling of Natural Phenomena 5.7 (2010): 11-15. <http://eudml.org/doc/197642>.

@article{Boujena2010,
abstract = {Plant growth depends essentially on nutrients coming from the roots and metabolites produced by the plant. Appearance of new branches is determined by concentrations of certain plant hormones. The most important of them are Auxin and Cytokinin. Auxin is produced in the growing, Cytokinin in either roots or in growing parts. Many dynamical models of this phenomena have been studied in [1]. In [5], the authors deal with one branch model. In this work, we focus our interest on a multiple branch model. We deal with the transport equation in domains of different sizes. A variational reduction type method [3] based on asymptotic partial decomposition introduced in [2] (see also [4]) is used. In this work we consider the transport equation in decomposed domain with a general right hand side},
author = {Boujena, S., Chiboub, A., Pousin, J.},
editor = {Taik, A.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {plant growth; transport equation; multiple branching plants; variational reduction; cells proliferation; concentration; hormone; displacement; nutrients; hormones; transport; domain decomposition; asymptotic expansion; MAPDD},
language = {eng},
month = {8},
number = {7},
pages = {11-15},
publisher = {EDP Sciences},
title = {Variational Reduction for the Transport Equation in a Multiple Branching Plants Growth Model},
url = {http://eudml.org/doc/197642},
volume = {5},
year = {2010},
}

TY - JOUR
AU - Boujena, S.
AU - Chiboub, A.
AU - Pousin, J.
AU - Taik, A.
TI - Variational Reduction for the Transport Equation in a Multiple Branching Plants Growth Model
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/8//
PB - EDP Sciences
VL - 5
IS - 7
SP - 11
EP - 15
AB - Plant growth depends essentially on nutrients coming from the roots and metabolites produced by the plant. Appearance of new branches is determined by concentrations of certain plant hormones. The most important of them are Auxin and Cytokinin. Auxin is produced in the growing, Cytokinin in either roots or in growing parts. Many dynamical models of this phenomena have been studied in [1]. In [5], the authors deal with one branch model. In this work, we focus our interest on a multiple branch model. We deal with the transport equation in domains of different sizes. A variational reduction type method [3] based on asymptotic partial decomposition introduced in [2] (see also [4]) is used. In this work we consider the transport equation in decomposed domain with a general right hand side
LA - eng
KW - plant growth; transport equation; multiple branching plants; variational reduction; cells proliferation; concentration; hormone; displacement; nutrients; hormones; transport; domain decomposition; asymptotic expansion; MAPDD
UR - http://eudml.org/doc/197642
ER -

References

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  1. N. Bessonov, V. Volpert. Dynamic models of plant growth. Mathematics and mathematical modeling I. Publibook Paris, (2007).  Zbl1151.92021
  2. G.P. Panasenko. Multi-scale modelling for structures and composites. Springer Verlag, (2005).  Zbl1078.74002
  3. O. Diallo. Modélisation et simulation numérique de résine réactive dans un milieu poreux. Thèse de doctorat, Université Claude Bernard Lyon 1, (2000).  
  4. F. Fontevieille. Décomposition asymptôtique et éléments finis. Thèse de doctorat, Université Claude Bernard Lyon 1, (2004).  
  5. M.Picq, J.Pousin.Variational reduction for the transport equation and plants growth. Proccedings of the conference modelling of the heterogeneous materials with applications in constructions and biological engineering, czech technical, University of Prague, (2007).  

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