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

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	821-826
Number of pages	6
Journal	Communications in Theoretical Physics
Volume	50
Issue number	4
DOIs	https://doi.org/10.1088/0253-6102/50/4/05
State	Published - 15 Oct 2008

Keywords

Exact solution
Invariant set
Nonlinear diffusion equations
Rotation group
Scaling group

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10.1088/0253-6102/50/4/05

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abstract = "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.",

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

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Keywords

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