A Model of Controlled Growth

Alberto Bressan, Marta Lewicka

Research output: Contribution to journalArticle

Abstract

We consider a free boundary problem for a system of PDEs, modeling the growth of a biological tissue. A morphogen, controlling volume growth, is produced by specific cells and then diffused and absorbed throughout the domain. The geometric shape of the growing tissue is determined by the instantaneous minimization of an elastic deformation energy, subject to a constraint on the volumetric growth. For an initial domain with C2 , α boundary, our main result establishes the local existence and uniqueness of a classical solution, up to a rigid motion.

Original languageEnglish (US)
Pages (from-to)1223-1266
Number of pages44
JournalArchive for Rational Mechanics and Analysis
Volume227
Issue number3
DOIs
StatePublished - Mar 1 2018

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Volume Growth
Biological Tissue
Elastic Deformation
Local Existence
Free Boundary Problem
Classical Solution
Tissue
Instantaneous
Existence and Uniqueness
Elastic deformation
Motion
Cell
Energy
Modeling
Model

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

Cite this

Bressan, Alberto ; Lewicka, Marta. / A Model of Controlled Growth. In: Archive for Rational Mechanics and Analysis. 2018 ; Vol. 227, No. 3. pp. 1223-1266.
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A Model of Controlled Growth. / Bressan, Alberto; Lewicka, Marta.

In: Archive for Rational Mechanics and Analysis, Vol. 227, No. 3, 01.03.2018, p. 1223-1266.

Research output: Contribution to journalArticle

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