  The paper introduces a PDE model for the growth of a tree stem or a vine. The
equations describe the elongation due to cell growth, and the response to
gravity and to external obstacles. An additional term accounts for the tendency
of a vine to curl around branches of other plants.
  When obstacles are present, the model takes the form of a differential
inclusion with unilateral constraints. At each time t, a cone of admissible
reactions is determined by the minimization of an elastic deformation energy.
The main theorem shows that local solutions exist and can be prolonged globally
in time, except when a specific "breakdown configuration" is reached.
Approximate solutions are constructed by an operator-splitting technique. Some
numerical simulations are provided at the end of the paper.
