| Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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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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