| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2021: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2020: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Outline of Final Research Achievements |
We study a general reaction-diffusion-ODE system, which consists of several ordinary differential equations coupled with a reaction-diffusion equation, in a bounded domain and with Neuman boundary condition. There are a lot of mathematical models in the form of a reaction-diffusion-ODE system, for example, models of pattern formation, and models of ecological dynamics.
It has been proved that all near-equilibrium (regular) patterns of a general reaction-diffusion-ODE system are unstable, regardless of the particular structure assumption on nonlinearities. This observation suggests that stable stationary solutions arising in models with non-diffusive components must be far-from-equilibrium exhibiting singularities. We have presented the existence of stationary solutions with jump-discontinuities and have provided sufficient conditions for their stability.
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