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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| Format: | Article |
| Language: | English |
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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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| _version_ | 1832559834327678976 |
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| author | Takasi Senba Takasi Suzuki |
| author_facet | Takasi Senba Takasi Suzuki |
| author_sort | Takasi Senba |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-61a6386baa69495585912015cf1c479c |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-61a6386baa69495585912015cf1c479c2025-02-03T01:29:02ZengWileyAbstract and Applied Analysis1085-33751687-04092006-01-01200610.1155/AAA/2006/2306123061A quasi-linear parabolic system of chemotaxisTakasi Senba0Takasi Suzuki1Department of Applied Mathematics, Faculty of Technology, Miyazaki University, 1-1 Gakuen Kibanadai Nishi, Miyazaki-shi 889-2192, JapanDepartment of Mathematical Science, Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama-machi, Toyonaka-shi 560-8531, JapanWe 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.http://dx.doi.org/10.1155/AAA/2006/23061 |
| spellingShingle | Takasi Senba Takasi Suzuki A quasi-linear parabolic system of chemotaxis Abstract and Applied Analysis |
| title | A quasi-linear parabolic system of chemotaxis |
| title_full | A quasi-linear parabolic system of chemotaxis |
| title_fullStr | A quasi-linear parabolic system of chemotaxis |
| title_full_unstemmed | A quasi-linear parabolic system of chemotaxis |
| title_short | A quasi-linear parabolic system of chemotaxis |
| title_sort | quasi linear parabolic system of chemotaxis |
| url | http://dx.doi.org/10.1155/AAA/2006/23061 |
| work_keys_str_mv | AT takasisenba aquasilinearparabolicsystemofchemotaxis AT takasisuzuki aquasilinearparabolicsystemofchemotaxis AT takasisenba quasilinearparabolicsystemofchemotaxis AT takasisuzuki quasilinearparabolicsystemofchemotaxis |