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