| Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2012: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Outline of Final Research Achievements |
The general theory for nonlinear wave equations is devoted to the estimate of the maximal existence time of classical solutions with small data. In high dimensions in which the spatial dimension is grater than 3, its optimality can be discussed only for the quadratic terms in four space dimensions. In such a case, the square of unknown functions itself is known to be a unique example of the nonlinear term which leads to the blow-up of the solution in finite time. The purpose of this study is to look for a criterion which classifies the nonlinear terms including the square of unknown functions into the global existence case or the blow-up case.
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