| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2020: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2019: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Outline of Final Research Achievements |
1, We consider the fifth order KdV type equations and prove the unconditional well-poseedness in the Sobolev space when its index is greater than or equal to 1. It is optimal in the sense that the nonlinear terms can not be defined in the space-time distribution framework when the index is less than 1. The main idea is to employ the normal form reduction and a kind of cancellation properties to deal with the derivative losses.
2, We consider the Cauchy problem of a class of higher order Schrodinger type equations with constant coefficients. By employing the energy inequality, we show the L2 well-posedness, the parabolic smoothing and a breakdown of the persistence of regularity. We classify this class of equations into three types on the basis of their smoothing property.
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