| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Outline of Final Research Achievements |
We consider the integral equation with respect to nonlinear diffusion equations, which are represented by semilinear heat equations, in the whole space. Under the condition that solutions of nonlinear integral equations behave like a multiple of the integral kernel asymptotically, we established the method of obtaining the higher order linear asymptotic expansions, which depends on the degree of moment of initial data, and nonlinear asymptotic expansion, which depends on the conditions for the nonlinear term. Furthermore, we applied our arguments to the heat equation with nonlinear boundary condition on the half space, nonlinear damped wave equations in the whole space and fractional diffusion equations in the whole space.
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