Application of variational inequalities to the moving-boundary problem in a fluid model for biofilm growth
Författare
Summary, in English
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
Publiceringsår
2009
Språk
Engelska
Sidor
3658-3664
Publikation/Tidskrift/Serie
Nonlinear Analysis: Theory, Methods & Applications
Volym
70
Issue
10
Dokumenttyp
Artikel i tidskrift
Förlag
Elsevier
Ämne
- Mathematics
Nyckelord
- variational inequality
- Moving-boundary problem
- Biofilm model
Status
Published
ISBN/ISSN/Övrigt
- ISSN: 0362-546X