| 边界退化的奇异扩散方程解的正则性 |
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| 引用本文： | 谢清梅,詹华税.边界退化的奇异扩散方程解的正则性[J].厦门水产学院学报,2011(5):389-391. |
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| 作者姓名： | 谢清梅 詹华税 |
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| 作者单位： | 集美大学理学院,福建厦门361021 |
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| 基金项目： | 福建省自然科学基金资助项目（2009J01009）; 集美大学科研基金资助项目（C510071） |
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| 摘 要： | 研究在边界退化的奇异扩散方程u/t=div（dα︱▽u︱p-2▽u）,（x,t）∈QT=Ω×（0,T）,其中ΩRN是一个边界适当光滑的有界区域,p〉1,α〉0,d（x）=dist（x,Ω）.在假设解的唯一性成立的前提下,证明了这种热传导问题的弱解具有与一般热传导问题的弱解相似的正则性.
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| 关 键 词： | 边界退化 扩散方程 唯一性 正则性 |
The Regular Properties of the Singular Diffusion Equation with Boundary Degeneracy |
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| Authors: | XIE Qing-mei ZHAN Hua-shui |
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| Institution: | (School of Science,Jimei University,Xiamen 361021,China) |
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| Abstract: | The singular diffusion equation with boundary degeneracy u/t=div（dα︱▽u︱p-2▽u）,（x,t）∈QT=Ω×（0,T） was studied,where ΩRN was bounded domain with appropriately smooth boundary,p1,α0,α≠1,and d（x）=dist（x,Ω）.Under the assumption on the uniqueness of the weak solution,the regular properties of the weak solution similar to those of the weak solution for a general heat conduction without degeneracy on the boundary were obtained. |
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| Keywords: | boundary degeneracy diffusion equation uniqueness regular property |
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