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

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Author

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

Publishing year

2009

Language

English

Pages

3658-3664

Publication/Series

Nonlinear Analysis: Theory, Methods & Applications

Volume

70

Issue

10

Document type

Journal article

Publisher

Elsevier

Topic

  • Mathematics

Keywords

  • variational inequality
  • Moving-boundary problem
  • Biofilm model

Status

Published

ISBN/ISSN/Other

  • ISSN: 0362-546X