| Project/Area Number |
23654059
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Global analysis
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| Research Institution | Tohoku University |
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Principal Investigator |
OGAWA Takayoshi 東北大学, 理学(系)研究科(研究院), 教授 (20224107)
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| Co-Investigator(Kenkyū-buntansha) |
NAGAI Toshitaka 広島大学, 大学院理学研究科, 名誉教授 (40112172)
KUROKIBA Masaki 室蘭工業大学, 大学院工学研究科, 准教授 (60291837)
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| Project Period (FY) |
2011-04-28 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 移流拡散方程式 / 質量輸送問題 / 非局所的相互作用 / 非線形偏微分方程式論 / 時間大域解 / 有限時刻爆発 / 不等式の最良定数 / 閾値 / 移流拡散方程式系 / 臨界最大正則性 / 変数係数放物型方程式 / 消散評価 / 解の有限時刻爆発 / Fisherの不等式 / 重み付き空間 / 非圧縮性粘性流体 / 退化移流拡散方程式 / 最大正則性原理 / ハーディー・リトルウッドの不等式 / 最良定数 / 線型熱方程式 / 斉次Besov空間 / 非局所放物型方程式 / 臨界指数 / 退化放物型 / 渦度Navier-Stokes方程式 / 非臨界指数 / 単極型移流拡散方程式 / 双極型移流拡散方程式 / 臨界型Sobolev不等式 / 退化放物 / Charn-Simons-Dirac / 適切性 / 圧縮性Euler-Poisson / 非線形熱方程式 |
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| Outline of Final Research Achievements |
Models described by drift-diffusion equations having a typical mass transport structure, it is understood and classified as one of the non-local interaction system. In this research, we consider the global behavior of the solution to a semi-linear drift-diffusion system in two and three-dimensional cases. In addition, we also study a system of degenerate drift-diffusion equations and make it clear the global behavior
of the weak solution. Furthermore, we find the global structure of the solutions are quite similar to the one of the nonlinear disspersive equations and between the critical exponents, we classified the global behavior of the solution and find the threshold value of the global existence.
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