A study on the asymptotic behavior of infinite-time blow up solutions for parabolic equations involving critical Hardy-Sobolev exponent
| Project/Area Number |
19740081
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Global analysis
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| Research Institution | Muroran Institute of Technology |
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Principal Investigator |
ISHIWATA Michinori Muroran Institute of Technology, 共生システム理工学類, 准教授 (30350458)
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| Project Period (FY) |
2007 – 2010
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥3,860,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2007: ¥1,000,000 (Direct Cost: ¥1,000,000)
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| Keywords | 臨界指数 / 漸近挙動 / コンパクト性の破れ / 無限時間爆発 / 臨界性 / トレース・ハーディ不等式 / 力学的境界条件 / エネルギーの量子化 / 関数方程式の大域理論 / ハーディの不等式 / トレース作用素 / ソボレフの不等式 / 藤田型方程式 / 無限時問爆発 / 放物型方程式 / 非線型偏微分方程式 / 非線形微分方程式 |
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| Research Abstract |
In this study, we are concerned with the profiles of infinite time blow-up solutions for semilinear parabolic equations involving critical Sobolev-Hardy exponents. For the critical Sobolev case, which is a special case of the critical Sobolev-Hardy case, we find that the asymptotic behavior of infinite time blow-up solutions are governed by the nontrivial stationary solutions of the equations. We also treat the several parabolic equations which are related with Hardy and Sobolev inequalities.
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Report
(6 results)
Research Products
(70 results)
