Reduction of reaction diffusion system and asymptotic analysis
| Project/Area Number |
17540125
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | University of Miyazaki |
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Principal Investigator |
TSUJIKAWA Tohru University of Miyazaki, Engineering, Professor (10258288)
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| Co-Investigator(Kenkyū-buntansha) |
SENBA Takashi Kyushu Institute of Technology, Engineering, Professor (30196985)
YAZAKAI Shigetoshi University of Miyazaki, Engineering, Associate professor (00323874)
YAGI Atsushi Osaka University, Engineering, Professor (70116119)
NAKAKI Tatsuyuki Hiroshima University, Integrated arts and sciences, Professor (50172284)
KABEYA Yoshitsugu Osaka Prefecture University, Engineering, Associate Professor (70252757)
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| Project Period (FY) |
2005 – 2007
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| Project Status |
Completed (Fiscal Year 2007)
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| Budget Amount *help |
¥3,170,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥270,000)
Fiscal Year 2007: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2006: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2005: ¥1,100,000 (Direct Cost: ¥1,100,000)
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| Keywords | Exponential Attractor / Reaction diffusion equation / Singular limit / Squeezing property / Bifurcation / Weakly interaction / Stability / Pattern formation / Interface analysis / Weakly Interaction / Traveling front solution / Kinematic model / Exponential Attractor / Interface / Chemotaxis / Phase Transition |
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| Research Abstract |
1. For the chemotaxis growth model
(1) Existence of a traveling front solution and its stability in a channel domain with Neumann boundary condition by using singular limit analysis
(2) Existence of a symmetric stationary solution and its stability in 3 dimensional space by using the reduction system
(3) Existence of time global non-negative solution and finite dimensional exponential attractor in the case of singular sensitivity function
(4) Instability of the non-negative constant solution and divergence of the dimension of the exponential attractor due to the increases of the chemotaxis effect
2. For the adsorbate-induced phase transition model
(1) Existence of time global non-negative solution and finite dimensional exponential attractor under periodic boundary condition in a finite segment
(2) Existence of time global non-negative solution and finite dimensional exponential attractor under Newmann boundary condition in 2dimensional finite domain with C^2 class boundary or convex domain
(3) Existence of the stripe and hexagonal stationary solutions due to the bifurcation from non-negative constant solution in the square domain with Newmann boundary condition
3. For the forest kinematic model
(1) Introduction of three kinds of omega limit sets and investigation of the basic property of these limit sets
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Report
(4 results)
Research Products
(34 results)
