| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Research Abstract |
I considered the Cauchy problem for second-order hyperbolic operators with the coefficients of their principal parts depending only on the time variable. In the case where the coefficients 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 part are semi-algebraic functions (e. g., polynomials) of the time variable. Moreover, under this sufficient condition I proved that the singularities of solutions to the Cauchy problem propagate along broken null bicharacteristics.
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