A quasi-linear parabolic system of chemotaxis
We consider a quasi-linear parabolic system with respect to unknown functions u and v on a bounded domain of n-dimensional Euclidean space. We assume that the diffusion coefficient of u is a positive smooth function A(u), and that the diffusion coefficient of v is a positive constant. If A(u) is a...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2006-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/AAA/2006/23061 |
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| Summary: | We consider a quasi-linear parabolic system with respect to
unknown functions u and v on a bounded domain of
n-dimensional Euclidean space. We assume that the diffusion
coefficient of u is a positive smooth function A(u), and that
the diffusion coefficient of v is a positive constant. If A(u)
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 A(u) rapidly increases with respect to
u. |
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| ISSN: | 1085-3375 1687-0409 |