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 引用本文: 石佩虎, 王明新. 带梯度吸收项的快扩散方程的自相似奇性解[J]. 应用数学和力学, 2007, 28(1): 99-106.
SHI Pei-hu, WANG Ming-xin. Self-Similar Singular Solution of Fast Diffusion Equation With Gradient Absorption Terms[J]. Applied Mathematics and Mechanics, 2007, 28(1): 99-106.
 Citation: SHI Pei-hu, WANG Ming-xin. Self-Similar Singular Solution of Fast Diffusion Equation With Gradient Absorption Terms[J]. Applied Mathematics and Mechanics, 2007, 28(1): 99-106.

带梯度吸收项的快扩散方程的自相似奇性解

作者简介:石佩虎(1967- ),男,湖南省花垣县人,副教授,博士(联系人.E-mail:sph2106@yahoo.com.cn).
• 中图分类号: O175.26

Self-Similar Singular Solution of Fast Diffusion Equation With Gradient Absorption Terms

• 摘要: 研究一类带有非线性梯度吸收项的快速扩散方程的自相似奇性解．通过自相似变换,该自相似奇性解满足一个非线性常微分方程的边值问题，再利用打靶法技巧研究该常微分方程初值问题解的存在唯一性并根据初值的取值范围对其解进行了分类．通过对这些解类的性质的分析研究，得出了自相似强奇性解存在唯一性的充分必要条件，此时自相似奇性解就是强奇性解．
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出版历程
• 收稿日期:  2004-05-28
• 修回日期:  2006-10-09
• 刊出日期:  2007-01-15

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