| Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
|
|---|
| Outline of Final Research Achievements |
I considered the Cauchy problem for higher-order hyperbolic operators with coefficients depending only on the time variable. In the case where the coefficients of the principal parts are real analytic functions of the time variable, I obtained a sufficient condition for C∞ well-posedness. And I showed that this sufficient condition is also a necessary one when the space dimension is less than 3 or the coefficients of the principal parts are semi-algebraic functions ( e.g., polynomials ) of the time variable. Moreover, in the case where the coefficients of the lower-order terms also depend on the space variables, I obtained a similar results under restrictions on the number of the double characteristic roots.
I gave sufficient conditions for C∞ well-posedness of the Cauchy problem for third-order hyperbolic operators whose coefficients depend only on the time variable, in the form of imposing conditions on the subprincipal symbols and the first-order terms.
|
