| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Outline of Final Research Achievements |
We show linear stability or instability for radially symmetric equilibrium solutions to the system of interface equation and two parabolic equations arising in the singular limit of three-component activator-inhibitor models.
Also, we study the free boundary problem describing the micro phase separation in the regime that one component has small volume fraction ρ such that the micro phase separation results in an ensemble of small disks of one component. We rigorously derive the heterogeneous mean-field equations on a time scale of the order of R^3 ln (1/ρ), where R is the mean radius of disks. On this time scale, the evolution is dominated by coarsening and stabilization of the radii of the disks, whereas migration of disks becomes only relevant on a larger time scale.
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