  Existence and uniqueness of solutions for a class of models for
stress-modulated growth is proven in one spatial dimension. The model features
the multiplicative decomposition of the deformation gradient $F$ into an
elastic part $F_e$ and a growth-related part $G$. After the transformation due
to the growth process, governed by $G$, an elastic deformation described by
$F_e$ is applied in order to restore the Dirichlet boundary conditions and
therefore the current configuration might be stressed with a stress tensor $S$.
The growth of the material at each point in the reference configuration is
given by an ordinary differential equation for which the right-hand side may
depend on the stress $S$ and the pull-back of a nutrient concentration in the
current configuration, leading to a coupled system of ordinary differential
equations.
