| Budget Amount *help |
¥14,040,000 (Direct Cost: ¥10,800,000、Indirect Cost: ¥3,240,000)
Fiscal Year 2014: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2013: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2012: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2011: ¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
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| Outline of Final Research Achievements |
The space-time estimates by Lindblad and Rodnianski were generalized, and the initial value problem was considered for the system of wave equations with nonlinear terms which satisfy the null conditions in three spatial dimensions. The initial value problem was considered for heat equations with derivative nonlinear terms in Besov spaces and Triebel-Lizorkin spaces. The energy solutions of the initial value problem were constructed for nonlinear Klein-Gordon equations in the de Sitter space-time, and nonlinear Schroedinger equations derived by its nonrelativistic limit. The best constant of the Moser-Trudinger inequality was shown in Lebesgue spaces with a weight which has a singularity, and it is applied to the initial value problem for nonlinear Klein-Gordon equations with nonlinear terms of exponential type.
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