Variational reduction for the transport equation in a multiple branching plants growth model

The plant growth and particularly the appearance of new branches is a consequence of the concentration of two hormones. One of them is produced in the roots and the other one is produced in the growing parts of the plant. Many dynamical models of this phenomena have already been studied. In this work we study a model of multiple branching. We deal with the transport equation in domains of different sizes by using a variational reduction type method based on the asymptotic partial decomposition for an elliptic problem. In general this is applied to the case of a geometrical heterogeneous domain when the right hand side does not depend on the striking variable. In our case we consider the transport equation in an heterogeneous domain with a general right hand side.