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Application of variational inequalities to the moving-boundary problem in a fluid model for biofilm growth

Overgaard, Niels Christian LU (2009) In Nonlinear Analysis: Theory, Methods & Applications 70(10). p.3658-3664
Abstract
We consider a moving-boundary problem associated with the fluid model for biofilm growth proposed by J. Dockery and I. Klapper, Finger formation in biofilm layers, SIAM J. Appl. Math. 62 (3) (2001) 853–869. Notions of classical, weak, and variational solutions for this problem are introduced. Classical solutions with radial symmetry are constructed, and estimates for their growth given. Using a weighted Baiocchi transform, the problem is reformulated as a family of variational inequalities, allowing us to show that, for any initial biofilm configuration at time t=0 (any bounded open set), there exists a unique weak solution defined for all t≥0
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author
publishing date
type
Contribution to journal
publication status
published
subject
keywords
variational inequality, Moving-boundary problem, Biofilm model
in
Nonlinear Analysis: Theory, Methods & Applications
volume
70
issue
10
pages
3658 - 3664
publisher
Elsevier
external identifiers
  • scopus:61749091183
ISSN
0362-546X
DOI
10.1016/j.na.2008.07.021
language
English
LU publication?
no
id
df6da4f9-b543-47b8-aa76-a8d57652a024 (old id 1658197)
date added to LUP
2010-09-10 13:32:27
date last changed
2017-03-26 04:02:50
@article{df6da4f9-b543-47b8-aa76-a8d57652a024,
  abstract     = {We consider a moving-boundary problem associated with the fluid model for biofilm growth proposed by J. Dockery and I. Klapper, Finger formation in biofilm layers, SIAM J. Appl. Math. 62 (3) (2001) 853–869. Notions of classical, weak, and variational solutions for this problem are introduced. Classical solutions with radial symmetry are constructed, and estimates for their growth given. Using a weighted Baiocchi transform, the problem is reformulated as a family of variational inequalities, allowing us to show that, for any initial biofilm configuration at time t=0 (any bounded open set), there exists a unique weak solution defined for all t≥0},
  author       = {Overgaard, Niels Christian},
  issn         = {0362-546X},
  keyword      = {variational inequality,Moving-boundary problem,Biofilm model},
  language     = {eng},
  number       = {10},
  pages        = {3658--3664},
  publisher    = {Elsevier},
  series       = {Nonlinear Analysis: Theory, Methods & Applications},
  title        = {Application of variational inequalities to the moving-boundary problem in a fluid model for biofilm growth},
  url          = {http://dx.doi.org/10.1016/j.na.2008.07.021},
  volume       = {70},
  year         = {2009},
}