| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Research Abstract |
In this research, we are concerned with the asymptotic behavior of time-global solutions for semilinear parabplic equations whose Lyapnov functional are suffered from the lack of compactness, togehter with the elliptic problem with variational functional with lack of compactness. Also we studeid the variational problem (minimizing problem) associated with the critical functional inequalities such as Sobolev, Hardy and the Trudinger-Moser type.
As for the parabolic problems, we treated the semilinear parabolic problem involving critical Sobolev exponent and showed the energy quantization phenomena for the time-global solutions. Also we studied the elliptic problem defined in the exterior domain with bounded complement with weight function decaying at the spatial infinity. We proved that if the decay of the weight function is sufiiciently slow, then the equations have multiple positive solutions.
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