| 非线性拟抛物粘性扩散方程的显式精确解 |
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| 引用本文： | 尚亚东,黄勇.非线性拟抛物粘性扩散方程的显式精确解[J].广州大学学报(自然科学版),2011,10(2):1-5. |
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| 作者姓名： | 尚亚东 黄勇 |
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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,计算机科学与教育软件学院,广东广州510006 |
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| 基金项目： | 国家自然科学基金，广东省科技计划项目 |
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| 摘 要： | 研究了出现在人口动力学和稳定分层粘性湍动慢剪切流中热与质量传输理论的一类非线性拟抛物粘性扩散方程.借助于分离变量方法获得了所研究方程的一些精确解,包括整体光滑解和精确爆破解.这些解有助于定性或数值分析非线性拟抛物粘性扩散方程解的性态.
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| 关 键 词： | 非线性拟抛物方程 分离变量方法 精确解 整体光滑解 爆破解 |
Explicit and exact solutions to the nonlinear pseudo-parabolic viscous diffusion equation |
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| SHANG Ya-dong,HUANG Yong.Explicit and exact solutions to the nonlinear pseudo-parabolic viscous diffusion equation[J].Journal og Guangzhou University:Natural Science Edition,2011,10(2):1-5. |
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| Authors: | SHANG Ya-dong HUANG Yong |
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| Institution: | b (a.School of Mathematics and Information Sciences;b.School of Computer Science and Educational Software,Guangzhou University,Guangzhou 510006,China) |
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| Abstract: | This paper studies a class of nonlinear pseudo-parabolic viscous diffusion equation which arises in population dynamics and in the theory of heat and mass transfer in stably stratified turbulent shear and slow viscous flows.With the aid of method of separation of variables,we obtain some exact solutions of the equation.These solutions include the global smooth solutions and exact blow up solutions.They are helpful to analyze the behavior of solutions of nonlinear pseudo-parabolic viscous diffusion equation qualitatively and numerically. |
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| Keywords: | nonlinear pseudo-parabolic viscous diffusion equation method of separation of variables exact solutions global smooth solutions blow up solutions |
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