| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Outline of Final Research Achievements |
Our research handles a free boundary problem for reaction-diffusion equations. This problem models spreading and migrating phenomena of a biological species and the main issue is to know asymptotic behaviors of the population density of the species and the boundary (free boundary) of its habitat. It is assumed that the density is governed by a reaction-diffusion equation and that the dynamics of the free boundary is determined by the Stefan condition. Since these free boundary problems were proposed by Du and Lin in 2010, a lot of people have studied them. We have discussed a reaction-diffusion equation with positive bistable reaction term which has two positive and stable equilibrium points and found out that a new type of asymptotic behaviors occurs for the free boundary problem. Moreover, we also have succeeded in getting theoretical understanding how the population density and habitat of the species change according as time goes on.
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