Characterization of positive solutions of the unstirred chemostat with an inhibitor

✍ Scribed by Hua Nie; Hongwei Zhang; Jianhua Wu

• Book ID: 103864350
• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 207 KB
• Volume: 9
• Category: Article
• ISSN: 1468-1218
• DOI: 10.1016/j.nonrwa.2007.01.018

✦ Synopsis

This paper deals with the unstirred chemostat model in the presence of an internal inhibitor. The main purpose of the paper is to determine the exact range of the maximal growth (a, b) of two species where the system possesses positive solutions. It turns out that is a connected unbounded region in R 2 + , whose boundary consists of two monotone nondecreasing curves 1 : a = H 1 (b) and 2 : b = H 2 (a). For every (a, b) inside the system has positive solutions and for (a, b) outside there exists no positive solution. The functions H 1 (b) and H 2 (a) are constructed in terms of the limit of the corresponding time-dependent solution with a specific initial function. In particular, it is also shown that the system has at least two positive solutions in certain subregion of .