| 具幂律扩散性非线性扩散方程的精确解 |
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| 引用本文： | 尚亚东.具幂律扩散性非线性扩散方程的精确解[J].广州大学学报(综合版),2013(6):1-8. |
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| 作者姓名： | 尚亚东 |
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| 作者单位： | [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 |
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| 基金项目： | This work was supported by NNSF （10771041,40890150,40890153） and Scientific Project of Guangdong Province （ 2008 B080701042 ） |
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| 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．
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| 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 |
Exact solutions for the nonlinear diffusion equations with power law diffusivity |
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| SHANG Ya-dong.Exact solutions for the nonlinear diffusion equations with power law diffusivity[J].Journal of Guangzhou University,2013(6):1-8. |
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| Authors: | SHANG Ya-dong |
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| Institution: | SHANG Ya-dong ( a. School of Mathematics and Information Sciences ; b. Key Laboratory of Mathematics and Interdisciplinary Seiences of Guangdong Higher Education Institute, Guangzhou University, Guangzhou 510006, China) |
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| Abstract: | 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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| Keywords: | nonlinear diffusion equation power law diffusivity separation of variables similarity transforma-tion explicit exact solutions |
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