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

¹ Department of Mathematics and Informatique, Faculty of Sciences Ain Chock, B.P 5366, Maarif 20200, Casablanca - Morocco
² INSA of Lyon, Institute Camille Jordan, UMR 5208, 69100 Villeurbanne, France

^* Corresponding author: E-mail: boujena@yahoo.fr

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