Separation of variables and exact solutions to nonlinear diffusion equations with x-dependent convection and absorption

Huabing Jia; Wei Xu; Xiaoshan Zhao; Zhanguo Li

doi:10.1016/j.jmaa.2007.07.063

Separation of variables and exact solutions to nonlinear diffusion equations with x-dependent convection and absorption

Huabing Jia
, Wei Xu
, Xiaoshan Zhao
, Zhanguo Li

School of Mathematics and Statistics

Northwestern Polytechnical University Xian

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

17 Scopus citations

Abstract

This paper considers nonlinear diffusion equations with x-dependent convection and source terms: u_t = (D (u) u_x)_x + Q (x, u) u_x + P (x, u). The functional separation of variables of the equations is studied by using the generalized conditional symmetry approach. We formulate conditions for such equations which admit the functionally separable solutions. As a consequence, some exact solutions to the resulting equations are constructed. Finally, we consider a special case for the equations which admit the functionally separable solutions when the convection and source terms are independent of x.

Original language	English
Pages (from-to)	982-995
Number of pages	14
Journal	Journal of Mathematical Analysis and Applications
Volume	339
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2007.07.063
State	Published - 15 Mar 2008

Keywords

Exact solutions
Generalized conditional symmetry
Nonlinear diffusion equations
Separation of variables

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10.1016/j.jmaa.2007.07.063

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title = "Separation of variables and exact solutions to nonlinear diffusion equations with x-dependent convection and absorption",

abstract = "This paper considers nonlinear diffusion equations with x-dependent convection and source terms: ut = (D (u) ux)x + Q (x, u) ux + P (x, u). The functional separation of variables of the equations is studied by using the generalized conditional symmetry approach. We formulate conditions for such equations which admit the functionally separable solutions. As a consequence, some exact solutions to the resulting equations are constructed. Finally, we consider a special case for the equations which admit the functionally separable solutions when the convection and source terms are independent of x.",

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author = "Huabing Jia and Wei Xu and Xiaoshan Zhao and Zhanguo Li",

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T1 - Separation of variables and exact solutions to nonlinear diffusion equations with x-dependent convection and absorption

AU - Jia, Huabing

AU - Xu, Wei

AU - Zhao, Xiaoshan

AU - Li, Zhanguo

PY - 2008/3/15

Y1 - 2008/3/15

N2 - This paper considers nonlinear diffusion equations with x-dependent convection and source terms: ut = (D (u) ux)x + Q (x, u) ux + P (x, u). The functional separation of variables of the equations is studied by using the generalized conditional symmetry approach. We formulate conditions for such equations which admit the functionally separable solutions. As a consequence, some exact solutions to the resulting equations are constructed. Finally, we consider a special case for the equations which admit the functionally separable solutions when the convection and source terms are independent of x.

AB - This paper considers nonlinear diffusion equations with x-dependent convection and source terms: ut = (D (u) ux)x + Q (x, u) ux + P (x, u). The functional separation of variables of the equations is studied by using the generalized conditional symmetry approach. We formulate conditions for such equations which admit the functionally separable solutions. As a consequence, some exact solutions to the resulting equations are constructed. Finally, we consider a special case for the equations which admit the functionally separable solutions when the convection and source terms are independent of x.

KW - Exact solutions

KW - Generalized conditional symmetry

KW - Nonlinear diffusion equations

KW - Separation of variables

UR - https://www.scopus.com/pages/publications/35348960427

U2 - 10.1016/j.jmaa.2007.07.063

DO - 10.1016/j.jmaa.2007.07.063

M3 - 文章

AN - SCOPUS:35348960427

SN - 0022-247X

VL - 339

SP - 982

EP - 995

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Separation of variables and exact solutions to nonlinear diffusion equations with x-dependent convection and absorption

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Keywords

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