Invariant sets and exact solutions to nonlinear diffusion equations with x-dependent convection and absorption

Hua Bing Jia; Wei Xu

doi:10.1088/0253-6102/50/4/05

Invariant sets and exact solutions to nonlinear diffusion equations with x-dependent convection and absorption

Hua Bing Jia
, Wei Xu

数学与统计学院

Northwestern Polytechnical University Xian
Baoji University of Arts and Sciences

科研成果: 期刊稿件 › 文章 › 同行评审

摘要

In this paper, we introduce a new invariant set , where f and g are some smooth functions of x, ε is a constant, and F is a smooth function to he determined. The invariant sets and exact solutions to nonlinear diffusion equation u_t (D(u)u_x)_x +Q(x,u)u_x +P{x,u), are discussed. It is shown that there exist several classes of solutions to the equation that belong to the invariant set o.

源语言	英语
页（从-至）	821-826
页数	6
期刊	Communications in Theoretical Physics
卷	50
期	4
DOI	https://doi.org/10.1088/0253-6102/50/4/05
出版状态	已出版 - 15 10月 2008

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N2 - In this paper, we introduce a new invariant set , where f and g are some smooth functions of x, ε is a constant, and F is a smooth function to he determined. The invariant sets and exact solutions to nonlinear diffusion equation ut (D(u)ux)x +Q(x,u)ux +P{x,u), are discussed. It is shown that there exist several classes of solutions to the equation that belong to the invariant set o.

AB - In this paper, we introduce a new invariant set , where f and g are some smooth functions of x, ε is a constant, and F is a smooth function to he determined. The invariant sets and exact solutions to nonlinear diffusion equation ut (D(u)ux)x +Q(x,u)ux +P{x,u), are discussed. It is shown that there exist several classes of solutions to the equation that belong to the invariant set o.

KW - Exact solution

KW - Invariant set

KW - Nonlinear diffusion equations

KW - Rotation group

KW - Scaling group

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JO - Communications in Theoretical Physics

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Invariant sets and exact solutions to nonlinear diffusion equations with x-dependent convection and absorption

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