Growth models for tree stems and vines

Alberto Bressan, Michele Palladino, Wen Shen

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


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 state 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.

Original languageEnglish (US)
Pages (from-to)2280-2316
Number of pages37
JournalJournal of Differential Equations
Issue number4
StatePublished - Aug 15 2017

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics


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