| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Outline of Final Research Achievements |
In these researches we studied asymptotiic profiles and optimal estimates in time of solutions (as time goes to infinity) to wave and/or plate equations with various damping mechanisms. The optimality implies the lower and upper bound of solutions with respect to time variable. In particular, it should be emphasized that the obtained lower bound in time of solutions is quite new in this type of wave equation field. Furthermore, by considering the exterior mixed problems for wave equations with/without damping mechanisms we investigated the total and/or local energy decay property, and especially in the case of nonlinear problems with power type nonlinearity of the corresponding problems for damped waves we determined the so-called critical exponent in the two dimensional case. Additionally, we remarked that the rate of decay of the local energy is much faster than those already known facts to the wave equation with non-smooth propagation speed.
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