Study on asymmetry and anisotropy in blow-up theory for nonlinear parabolic equations
| Project/Area Number |
23654064
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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 | Waseda University |
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Principal Investigator |
OZAWA Tohru 早稲田大学, 理工学術院, 教授 (70204196)
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| Co-Investigator(Kenkyū-buntansha) |
YAMAUCHI Yusuke 早稲田大学, 重点領域研究機構, 次席研究員 (00451435)
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| Co-Investigator(Renkei-kenkyūsha) |
MAEKAWA Yasunori 神戸大学, 理学研究科, 准教授 (70507954)
TANAKA Kazunaga 早稲田大学, 理工学術院, 教授 (20188288)
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| Project Period (FY) |
2011 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2011: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | 関数方程式の大域理論 / 解の爆発 / 非線型放物型方程式 |
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| Research Abstract |
Blow-up phenomenon of positive solutions to the Cauchy problem for nonlinear heat equation of Fujita type is studied. The blow-up phenomenon was first observed and proved by Hiroshi Fujita about half a century ago. There is a large literature on the subject, especially on the formation of blow-up solutions in configuration space up to the blow-up time. We have proved that the blow-up time is characterized by means of the spherical average of the Cauchy data. We removed the assumptions of uniformity and isotropy on the Cauchy data, which were necessary in the former works by Lee and Ni (Trans. Ams, 1992) and Gui and Wang (JDE 1995). We described how the ODE structure controls the blow-up phenomenon.
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Report
(3 results)
Research Products
(27 results)
