2013 Fiscal Year Final Research Report
Mechanism of reaction-diffusion systems modeling pattern formation phenomena in biology
| Project/Area Number |
23740118
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Global analysis
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| Research Institution | Ibaraki University (2012-2013)
Tohoku University (2011) |
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Principal Investigator |
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| Project Period (FY) |
2011-04-28 – 2014-03-31
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| Keywords | 反応拡散系 / 自己組織化 / 関数方程式論 |
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| Research Abstract |
There are some mathematical models of a pattern formation arising in processes described by a system of a single reaction-diffusion equation coupled with an ordinary differential equation. Such systems arise from modeling of interactions between cellular processes and diffusing growth factors, and exhibit the diffusion-driven instability.
In this study, a general reaction-diffusion-ODE system with a single diffusion operator is considered. First, I studied the instability of inhomogeneous stationary solutions. It was shown that a certain natural (autocatalysis) property of a system led to instability of all inhomogeneous stationary solutions. Next, I considered a possible large time behavior of solutions. It was seen that space inhomogeneous solutions of the system became unbounded in either finite or infinite time, even if space homogeneous solutions were bounded uniformly in time.
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Research Products
(20 results)
