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

✍ Scribed by Niels Chr. Overgaard

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 536 KB
• Volume: 70
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2008.07.021

✦ Synopsis

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.