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具幂律扩散性非线性扩散方程的精确解
  • ISSN号：0023-074X
  • 期刊名称：《科学通报》
  • 时间：0
  • 分类：O175.29[理学—数学;理学—基础数学]
  • 作者机构：[1]广州大学数学与信息科学学院,广东广州510006, [2]广州大学广东省教育厅数学与交叉科学重点实验室,广东广州510006
  • 相关基金：This work was supported by NNSF （10771041,40890150,40890153） and Scientific Project of Guangdong Province （ 2008 B080701042 ）
作者： 尚亚东[1,2]
关键词： 非线性扩散方程, 幂律扩散性, 分离变量, 相似变换, 显式精确解, nonlinear diffusion equation, power law diffusivity, separation of variables, similarity transforma-tion, explicit exact solutions
中文摘要：

提出了通过分离变量方法和相似变换获得带有幂律扩散性的一类非线性扩散方程显式精确解的框架，进而获得了某些重要的幂律扩散性物理过程的丰富的显式精确解．进一步考察了某些解的行为和爆破性质，推广补充了先前文献中的已知结果．

英文摘要：

In this paper, we develop a framework to obtain explicit and exact solutions to a class of nonlinear diffusion equations with power law diffusivity by employing the method of separation of variables and similarity transformation. Abundant explicit and exact solutions are obtained for some important physical processes of pow- er law diffusivity. The behavior and blow up properties of some solutions are investigated. The known results in previous literatures are supplemented and extended greatly.

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期刊信息
  • 《科学通报》
  • 北大核心期刊（2011版）
  • 主管单位:中国科学院
  • 主办单位:中国科学院
  • 主编：周光召
  • 地址：北京东黄城根北街16号
  • 邮编：100717
  • 邮箱：csb@scichina.org
  • 电话：010-64036120 64012686
  • 国际标准刊号：ISSN：0023-074X
  • 国内统一刊号：ISSN：11-1784/N
  • 邮发代号:80-213
  • 获奖情况:
  • 首届国家期刊奖,中国期刊方阵“双高”期刊,第三届中国出版政府奖
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  • 被引量:81792