2009 Fiscal Year Final Research Report
Spatio-Temporal Patterns and Finite-Dimensional Dynamical System generated by a Reaction-Diffusion Chemotaxis System
| Project/Area Number |
19740093
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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 | Ube National College of Technology |
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Principal Investigator |
OSAKI Koichi Ube National College of Technology, 理工学部, 准教授 (40353320)
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| Project Period (FY) |
2007 – 2009
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| Keywords | 非線形微分方程式 / 反応拡散方程式 / パターン形成 |
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| Research Abstract |
We examined the Mimura-Tsujikawa system, associated with advection due to chemotaxis, and global existence, blow-up and the pattern formation of solutions. The global existence of solutions was demonstrated by newly introducing a secretion term in a two-dimensional domain. We proved the blow-up of solutions only for the parabolic-elliptic approximated system by using the method of Jager-Luckhaus (Jager-Luckhaus, Trans. Amer. Math. Soc. 329(1992)). The pattern formation of the solutions was investigated by the reduction employing the center manifold theory. In the resulting solution, a constant solution was transversally bifurcated to an unstable hexagonal pattern solution, after which the bifurcated branches were inverted and become stable and simultaneously the stripe pattern solution caused an unstable pitch fork bifurcation.
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