| EXISTENCE AND NONEXISTENCE OF GLOBAL SOLUTION OF NONLINEAR PARABOLIC EQUATION WITH NONLINEAR BOUNDARY CONDITION |
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| 引用本文： | Wu Yonghui,Wang Mingxin. EXISTENCE AND NONEXISTENCE OF GLOBAL SOLUTION OF NONLINEAR PARABOLIC EQUATION WITH NONLINEAR BOUNDARY CONDITION[J]. 数学年刊B辑(英文版), 1995, 16(3): 371-378 |
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| 作者姓名： | Wu Yonghui Wang Mingxin |
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| 作者单位： | Institute of Systems Science，Academia Sinica，Be1Jing 100080，China.Institute of Applied Mathematics，Academia Sinica，Beijing 100080，China，and Department of Mathe mattes，Southeast Universityt Naming 210018，China. |
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| 摘 要： | ＥＸＩＳＴＥＮＣＥＡＮＤＮＯＮＥＸＩＳＴＥＮＣＥＯＦＧＬＯＢＡＬＳＯＬＵＴＩＯＮＯＦＮＯＮＬＩＮＥＡＲＰＡＲＡＢＯＬＩＣＥＱＵＡＴＩＯＮＷＩＴＨＮＯＮＬＩＮＥＡＲＢＯＵＮＤＡＲＹＣＯＮＤＩＴＩＯＮ￥ＷＵＹＯＮＧＨＵＩ；ＷＡＮＧＭＩＮＧＸＩＮＡｂｓｔｒ...
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| 关 键 词： | 存在性 全局解 非线性 抛物型偏微分方程 边界条件 |
| 收稿时间： | 1993-01-03 |
EXISTENCE AND NONEXISTENCE OF GLOBAL SOLUTION OF NONLINEAR PARABOLIC EQUATION WITH NONLINEAR BOUNDARY CONDITION |
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| Wu Yonghui and Wang Mingxin. EXISTENCE AND NONEXISTENCE OF GLOBAL SOLUTION OF NONLINEAR PARABOLIC EQUATION WITH NONLINEAR BOUNDARY CONDITION[J]. Chinese Annals of Mathematics,Series B, 1995, 16(3): 371-378 |
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| Authors: | Wu Yonghui and Wang Mingxin |
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| Affiliation: | Institute of Systems Science, Academia Sinica,Beijing 100080, China. and Institute of Applied Mathematics, Academia Sinica,Beijing 100080, China, and Department of Mathe-newlinetext{ } matics, SoutheastUniversity, Nanjing 210018, China |
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| Abstract: | This paper deals with the existence and nonexistence of global positivesolution of the following equation:$$ cases u_t=nabla(u^{q-1}nabla u)- a u^m, qquad & xin o, t>0,dfrac {partial u}{partial n} =u^p, &xin po, t>0,u(x, 0)=u_0(x)>0, &xin baro,endcases$$where $p, q, m, a$ are parameters with $qge 1, m, p >0, age 0. osubsetR^N$ is abounded domain with $po$ smooth enough, $ Nge 1.$ Thenecessary and sufficientconditions for the global existence of solution are obtained. |
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| Keywords: | Nonlinear parabolic equiation Nonlinear boundary condition Existence Blow-up Subsolution and supersolution. |
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