Application of variational inequalities to the moving-boundary problem in a fluid model for biofilm growth
(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
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1658197
- author
- Overgaard, Niels Christian LU
- publishing date
- 2009
- 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
- 2016-04-01 14:36:18
- date last changed
- 2022-02-27 03:34:19
@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}}, keywords = {{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}}, doi = {{10.1016/j.na.2008.07.021}}, volume = {{70}}, year = {{2009}}, }