Feedback Stabilization of Stem Growth
The paper studies a PDE model describing the elongation of a plant stem and its bending as a response to gravity. For a suitable range of parameters in the defining equations, it is proved that a feedback response produces stabilization of growth, in the vertical direction.
KeywordsFeedback stabilization First order PDE Stable linear semigroup Stem growth
The first author was partially supported by the Istituto Nazionale di Alta Matematica “F.Severi”, through GNAMPA. The research of the second author was partially supported by NSF, with Grant DMS-1714237 “Models of controlled biological growth”. The third author thanks the Agence Nationale de la Recherche for its financial support, with Projects DYFICOLTI (Grant ANR-13-BS01-0003-01) and IFSMACS (Grant ANR-15-CE40-0010). This work was initiated while the first and third authors were visiting the Department of Mathematics at Penn State University, which they thank for the kind hospitality.
- 2.Bressan, A., Palladino, M.: Well-posedness of a model for the growth of tree stems and vines. Discrete Contin. Dyn. Syst., to appearGoogle Scholar
- 5.Leyser, O., Day, S.: Mechanisms in Plant Development. Blackwell Publishing, Hoboken (2003)Google Scholar
- 6.Martin Jr., R.: Functional Analysis and Differential Equations in Banach Spaces. Wiley, Hoboken (1975)Google Scholar