2013 Fiscal Year Final Research Report
Global Existence and Pattern Formation of Solutions to a Reaction-Diffusion-Chemotaxis System
| Project/Area Number |
22740112
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Global analysis
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| Research Institution | Kwansei Gakuin University |
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Principal Investigator |
OSAKI Koichi 関西学院大学, 理工学部, 教授 (40353320)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | 走化性 / 反応拡散系 / パターン形成 / 非線形現象 / Keller-Segel系 |
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| Research Abstract |
We examined a chemotaxis system with a logistic growth, and global existence and the pattern formation of solutions. For the two- and three-dimensional cases, the global existence of solutions and the existence of exponential attractors were demonstrated by introducing a sublinear secretion term. The two- and three-dimensional pattern formation of the solutions also were investigated by the local bifurcation and the center manifold theory. We studied asymptotic behavior of the stationary solutions to the chemotaxis system, as the chemotactic coefficient tended to infinity.
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