| Project/Area Number |
08640223
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
解析学
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| Research Institution | Nagasaki Institute of Applied Science |
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Principal Investigator |
KAJIKIYA Ryuji Nagasaki Institute of Applied Science, Faculty of Engineering, Professor, 工学部, 教授 (10183261)
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| Co-Investigator(Kenkyū-buntansha) |
SENBA Takasi Miyazaki University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (30196985)
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| Project Period (FY) |
1996 – 1998
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| Project Status |
Completed (Fiscal Year 1998)
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| Budget Amount *help |
¥2,300,000 (Direct Cost: ¥2,300,000)
Fiscal Year 1998: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1997: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 1996: ¥900,000 (Direct Cost: ¥900,000)
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| Keywords | nonlinear elliptic equation / group invariant solution / variational method / blow-up / parabolic system / chemotaxis / parabelic system / 走化性 / 生物モデル |
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| Research Abstract |
1. We study the Emden-Fowler equation, which is one of partial differential equations of elliptic type, in a ball or annulus of <planck's constant>-dimensional Euclid space. Let C be a closed subgroup of the orthogonal group 0(<planck's constant>). A solution mu(x) of the equation is called G invariant if mu is invariant under G action. Any radial solution becomes G invariant. The converse problem is considered. The group G is a transformation group on the unit sphere because G is a subgroup of the orthogonal group. We prove that there exists a G invariant non-radial solution if and only if G is not transitive on the unit sphere. This result is proved by using variational method, functional analysis, Lie transformation group and Sturm-Liouville theory of ordinary differential
2. We study the Keller-Segel equation which is a mathematical model to describe a cellular slime having the oriented movement.
(1)A parabolic system which is a simplification of the Keller-Segel equation is considered. When a sensitive function is linear and the space dimension is two, the asymptotic behavior of a blow-up solution is investigated in detail.
(2)It is proved that a radial solution blows up as its L^1 density concentrates at the origin.
(3)The L^1 total mass of a solution is chosen as a parameter. Then the existence and non existence results of non-constant stationary solutions are obtained by using the parameter.
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