TY - JOUR
T1 - Well-posedness of a model for the growth of tree stems and vines
AU - Bressan, Alberto
AU - Palladino, Michele
N1 - Funding Information:
This research was partially supported by NSF grant DMS-1714237, "Models of controlled biological growth".
PY - 2018/4
Y1 - 2018/4
N2 - 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.
AB - 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.
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U2 - 10.3934/dcds.2018083
DO - 10.3934/dcds.2018083
M3 - Article
AN - SCOPUS:85041093662
SN - 1078-0947
VL - 38
SP - 2047
EP - 2064
JO - Discrete and Continuous Dynamical Systems- Series A
JF - Discrete and Continuous Dynamical Systems- Series A
IS - 4
ER -