TY - JOUR
T1 - A Model of Controlled Growth
AU - Bressan, Alberto
AU - Lewicka, Marta
N1 - Funding Information:
Acknowledgements. The first author was partially supported by NSF Grant DMS-1714237, “Models of controlled biological growth”. The second author was partially supported by NSF Grants DMS-1406730 and DMS-1613153.
Publisher Copyright:
© 2017, Springer-Verlag GmbH Germany.
PY - 2018/3/1
Y1 - 2018/3/1
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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U2 - 10.1007/s00205-017-1183-3
DO - 10.1007/s00205-017-1183-3
M3 - Article
AN - SCOPUS:85031400046
SN - 0003-9527
VL - 227
SP - 1223
EP - 1266
JO - Archive for Rational Mechanics and Analysis
JF - Archive for Rational Mechanics and Analysis
IS - 3
ER -