Well-posedness of a model for the growth of tree stems and vines

Alberto Bressan, Michele Palladino

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


The paper studies a PDE model for the growth of a tree stem or a vine, having the form of a differential inclusion with state constraints. The equations describe the elongation due to cell growth, and the response to gravity and to external obstacles. The main theorem shows that the evolution problem is well posed, until a specific "breakdown configuration" is reached. A formula is proved, characterizing the reaction produced by unilateral constraints. At a.e. time t, this is determined by the minimization of an elastic energy functional under suitable constraints.

Original languageEnglish (US)
Pages (from-to)2047-2064
Number of pages18
JournalDiscrete and Continuous Dynamical Systems- Series A
Issue number4
StatePublished - Apr 2018

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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