Extended rotation and scaling groups for nonlinear diffusion equations

Huabing Jia; Wei Xu

doi:10.1016/j.na.2007.06.004

Extended rotation and scaling groups for nonlinear diffusion equations

Huabing Jia
, Wei Xu

数学与统计学院

Northwestern Polytechnical University Xian

科研成果: 期刊稿件 › 文章 › 同行评审

摘要

In this paper, we introduce a new nonlinear extension to the rotation and scaling groups, which is described by the invariant set E = {u : u_x = f (x) F (u) + ε F (u) exp (- ∫^u frac(1, F (z)) d z)}. The invariant set and the exact solutions to the nonlinear diffusion equation u_t = (A (u) u_x)_x + Q (x, u) u_x + P (x, u), are discussed. It is shown that there exists a class of solutions to the equation that belong to the invariant set E. The invariant set is also used to construct exact solutions to some other nonlinear evolution equations.

源语言	英语
页（从-至）	592-611
页数	20
期刊	Nonlinear Analysis, Theory, Methods and Applications
卷	69
期	2
DOI	https://doi.org/10.1016/j.na.2007.06.004
出版状态	已出版 - 15 7月 2008

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N2 - In this paper, we introduce a new nonlinear extension to the rotation and scaling groups, which is described by the invariant set E = {u : ux = f (x) F (u) + ε F (u) exp (- ∫u frac(1, F (z)) d z)}. The invariant set and the exact solutions to the nonlinear diffusion equation ut = (A (u) ux)x + Q (x, u) ux + P (x, u), are discussed. It is shown that there exists a class of solutions to the equation that belong to the invariant set E. The invariant set is also used to construct exact solutions to some other nonlinear evolution equations.

AB - In this paper, we introduce a new nonlinear extension to the rotation and scaling groups, which is described by the invariant set E = {u : ux = f (x) F (u) + ε F (u) exp (- ∫u frac(1, F (z)) d z)}. The invariant set and the exact solutions to the nonlinear diffusion equation ut = (A (u) ux)x + Q (x, u) ux + P (x, u), are discussed. It is shown that there exists a class of solutions to the equation that belong to the invariant set E. The invariant set is also used to construct exact solutions to some other nonlinear evolution equations.

KW - Exact solution

KW - Nonlinear diffusion equation

KW - Rotation group

KW - Scaling group

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JO - Nonlinear Analysis, Theory, Methods and Applications

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ER -

Extended rotation and scaling groups for nonlinear diffusion equations

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