| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2021: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Outline of Final Research Achievements |
In this study, we consider scattering problems for nonlinear dispersive equations. We obtain the following results:
(1) We considered the 3-dim. Klein-Gordon equations whose nonlinearity is cubic, and we proved that the scattering operator maintain the smoothness and decay of the input data. (2) We considered the 2-dim. Klein-Gordon equations whose nonlinearity behaves like u(exp(|u|^2)-1), and we proved that the scattering operator maintain the smoothness and decay of the input data. (3) We considered the semi-relativistic equation whose interaction potential satisfies some suitable conditions, and we proved that the scattering operator maintain the smoothness and decay of the input data.
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