| Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Outline of Final Research Achievements |
We studied sufficient conditions for the existence of global solutions (solutions up to the arbitrary time) to the Cauchy problem for systems of nonlinear wave equations, or for some related systems, with small initial data. Concerning sufficient conditions weaker than the well-known null condition (such weaker conditions are called the "weak" null conditions), we unified the two known "weak" null conditions, and proved the global existence under this unified condition. Some formula to give the asymptotic behavior for global solutiuons was obtained. We also improved the global existence theorem by Alinhac for wave equations in two space dimensions. Concerning the systems of nolinear wave and Klein-Gordon equations, we proved the global existence of solutions under a weaker condition than before, in the case that initial data vanish outside a bounded region.
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