| Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Research Abstract |
The results are as follows. (1) We proved N-dimensional pyramidal traveling fronts in the Allen-Cahn (Nagumo) equation.(2) We consider the Allen-Cahn (Nagumo) equation in the three-dimensional space, and proved the existence and stability of cylindrically non-symmetric traveling fronts. The cross sections of these traveling fronts are smooth convex shapes, say, ellipses. (3) We prove the existence of N-dimensional pyramidal traveling fronts in competition-diffusion systems. (4) We prove the non-existence of localized traveling spots with non-zero speed in a single reaction-diffusion equation under some condition.
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