| PROPERTIES OF THE BOUNDARY FLUX OF A SINGULAR DIFFUSION PROCESS |
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| 作者姓名： | YIN Jingxue WANG Chunpeng |
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| 作者单位： | YIN JINGXUE WANG CHUNPENG Department of Mathematics，Jilin University，Changchun 130012，China. Department of Mathematics，Jilin University，Changchun 130012，China. |
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| 基金项目： | Project supported by the 973 Project of the Ministry of Science and Technology of China, the Outstanding Youth Foundation of China (No.10125107)，the Department of Mathematics of Jilin University. |
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| 摘 要： | The authors study the singular diffusion equationwhere Ω(?)Rn is a bounded domain with appropriately smooth boundary δΩ, ρ(x) = dist(x,δΩ), and prove that if α≥p-1, the equation admits a unique solution subject only to a given initial datum without any boundary value condition, while if 0 <α< p - 1, for a given initial datum, the equation admits different solutions for different boundary value conditions.
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| 关 键 词： | 边界线 奇异方程 唯一解 分布条件 |
| 收稿时间： | 4/3/2029 12:00:00 AM |
| 修稿时间： | 2020/10/3 0:00:00 |
PROPERTIES OF THE BOUNDARY FLUX OF A SINGULAR DIFFUSION PROCESS |
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| YIN Jingxue,WANG Chunpeng.PROPERTIES OF THE BOUNDARY FLUX OF A SINGULAR DIFFUSION PROCESS[J].Chinese Annals of Mathematics,Series B,2004,25(2):175-182. |
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| Authors: | YIN Jingxue and WANG Chunpeng |
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| Institution: | Department of Mathematics, Jilin University, Changchun 130012, China.;Department of Mathematics, Jilin University, Changchun 130012, China. |
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| Abstract: | The authors study the singular diffusion equation(6)u/(6)t = div(pα|(△)u|p-2(△)u), (x,t) ∈ QT = Ω× (0,T),where Ω (C) Rn is a bounded domain with appropriately smooth boundary (6)Ω, p(x) =dist(x, (6)Ω), and prove that if α≥ p- 1, the equation admits a unique solution subject only to a given initial datum without any boundary value condition, while if 0 ＜α＜p- 1, for a given initial datum, the equation admits different solutions for different boundary value conditions. |
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| Keywords: | Boundary flux Singular diffusion Boundary degeneracy |
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