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(2+1)维拟线性热方程的不变集和精确解 被引量：5

Invariant sets and solutions to (2+1) dimensional quasilinear heat equation
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摘要 目的研究带有反应项的(2+1)拟线性热方程ut=A(u)(uxx+Nx-1ux)+B(u)(uyy+N-1yuy)+C(u)u2x+D(u)u2y+Q(u)的精确解问题。方法运用推广的不变集E0={u:ux=vxF(u),uy=vyF(u)}求(2+1)维拟线性热方程的精确解。结果给出(2+1)维拟线性热方程的一些特殊解。结论此方法是(1+1)维拟线性热方程的推广。 Aim To study the exact solutions of （2 ＋ 1 ） dimensional quasilinear heat equation ut=A（u）（uxx＋N-1/xux）＋B（u）（uyy＋N-1/y uy,）＋C（u）ux^2＋D（u）uy^2＋Q（u）Methods Utilize the extended invariant set E0 ={u：ux=vxF（u）,uy=vyF（u）}to obtain the exact solutions of （2 ＋ 1 ） dimensional quasilinear heat equation.Results Some special exact solutions associated to the equation are obtained. Conclusion It is an extension to （ 1 ＋ 1 ） dimensional quasilinear heat equation.
作者 左苏丽 李吉娜 黄晴
机构地区 西北大学数学系
出处 《西北大学学报（自然科学版）》 CAS CSCD 北大核心 2007年第6期974-976,共3页 Journal of Northwest University（Natural Science Edition）
基金 国家自然科学基金资助项目(10671156)
关键词 伸缩群 旋转群 不变集 精确解 scaling group rotation group sign-invariant exact solution
分类号 O175.2 [理学—基础数学]
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参考文献7

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二级参考文献9

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共引文献4

同被引文献18

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  • 6Galaktionov V A. Groups of scalings and invariant sets for higher-order nonlinear evolution equation[J]. Differential Integeral Equations, 2001,14:913-924.
  • 7Galaktionov V A. Ordered invariant sets for nonlinear equations of KdV-type[J]. Compute. Math. Phys., 1999,39:1564-1570.
  • 8Qu C Z, Estevez P G. Extended rotation and scaling groups for nonlinear evolution equations[J]. Nonlinear Anal. TMA., 2003,52:1655-1673.
  • 9Zhu C R, Qu C Z. Invariant sets and solutions to higher-order reaction diffusion equation with source term[J]. Phys. Lett. A, 2006,354:437-444.
  • 10Qu C Z. Symmetries and solutions to the thin film equations[J]. Math. Anal. Appl., 2006,317:381-397.

引证文献5

二级引证文献6

西北大学学报（自然科学版）
2007年 第6期

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