Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2006 (2006), Article ID 23061, 21 pages.
A quasi-linear parabolic system of chemotaxis
We consider a quasi-linear parabolic system with respect to unknown functions and on a bounded domain of -dimensional Euclidean space. We assume that the diffusion coefficient of is a positive smooth function , and that the diffusion coefficient of is a positive constant. If is a positive constant, the system is referred to as so-called Keller-Segel system. In the case where the domain is a bounded domain of two-dimensional Euclidean space, it is shown that some solutions to Keller-Segel system blow up in finite time. In three and more dimensional cases, it is shown that solutions to so-called Nagai system blow up in finite time. Nagai system is introduced by Nagai. The diffusion coefficients of Nagai system are positive constants. In this paper, we describe that solutions to the quasi-linear parabolic system exist globally in time, if the positive function rapidly increases with respect to .
Abstr. Appl. Anal., Volume 2006 (2006), Article ID 23061, 21 pages.
First available in Project Euclid: 30 January 2007
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Senba, Takasi; Suzuki, Takasi. A quasi-linear parabolic system of chemotaxis. Abstr. Appl. Anal. 2006 (2006), Article ID 23061, 21 pages. doi:10.1155/AAA/2006/23061. https://projecteuclid.org/euclid.aaa/1170202966