A Model of Controlled Growth

Alberto Bressan; Marta Lewicka

doi:10.1007/s00205-017-1183-3

A Model of Controlled Growth

Alberto Bressan, Marta Lewicka

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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 language	English (US)
Pages (from-to)	1223-1266
Number of pages	44
Journal	Archive for Rational Mechanics and Analysis
Volume	227
Issue number	3
DOIs	https://doi.org/10.1007/s00205-017-1183-3
State	Published - Mar 1 2018

All Science Journal Classification (ASJC) codes

Analysis
Mathematics (miscellaneous)
Mechanical Engineering

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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.",

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N2 - 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.

AB - 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.

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A Model of Controlled Growth

Abstract

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