| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Outline of Final Research Achievements |
In this study, we consider some problems on scattering operators and analytic smoothing effects for nonlinear dispersive equations. Using the Method of functional analysis, we obtain the following results:
(1) We considered the one space dimensional Dirac equation with a p-th power nonlinearity, and we proved that if p is greater than 3 then the scattering operator can be defined on a neighborhood of 0 in a suitable Hilbert space. (2) We considered the three space dimensional Dirac equation with a cubic power nonlinearity, and we proved that a neighborhood of 0 in the weighted Sobolev space is included in the same weighted Sobolev space. (3) We considered the Hartee equation, and we proved some properties of the analytic smoothing effect.
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