Invariant Sets and Exact Solutions to Nonlinear Diffusion Equations with x-Dependent Convection and Absorption
作者： Jia Hua-Bing , Xu Wei
DOI: 10.1088/0253-6102/50/4/05
关键词: Invariant (mathematics) 、 Nonlinear diffusion equation 、 Convection 、 Physics 、 Mathematical physics 、 Nonlinear diffusion
摘要: In this paper, we introduce a new invariant set , where f and g are some smooth functions of x, e is constant, F function to he determined. The sets exact solutions nonlinear diffusion equation ut = (D(u)ux)x +Q(x,u)ux +P{x,u), discussed. It shown that there exist several classes the belong o.
harvard.edu
itp.ac.cn
sci-hub.se 参考文章(39)
Zhang Shun-Li, Lou Sen-Yue, Variable Separation and Derivative-Dependent Functional Separable Solutions to Generalized Nonlinear Wave Equations Communications in Theoretical Physics. ,vol. 41, pp. 161- 174 ,(2004) , 10.1088/0253-6102/41/2/161
Shun-Li Zhang, Sen-Yue Lou, Chang-Zheng Qu, Rui-Hong Yue, Classification and Functional Separable Solutions to Extended Nonlinear Wave Equations Communications in Theoretical Physics. ,vol. 44, pp. 589- 596 ,(2005) , 10.1088/6102/44/4/589
W. F. Ames, Nonlinear Partial Differential Equations in Engineering Physics Today. ,vol. 20, pp. 131- 131 ,(1967) , 10.1063/1.3034120
John Crank, The mathematics of diffusion ,(1956)
Changzheng Qu, P.G. Estévez, On nonlinear diffusion equations with x-dependent convection and absorption Nonlinear Analysis-theory Methods & Applications. ,vol. 57, pp. 549- 577 ,(2004) , 10.1016/J.NA.2004.02.027
Victor A. Galaktionov, Quasilinear heat equations with first-order sign-invariants and new explicit solutions Nonlinear Analysis-theory Methods & Applications. ,vol. 23, pp. 1595- 1621 ,(1994) , 10.1016/0362-546X(94)90208-9
Maria Luz Gandarias, Classical point symmetries of a porous medium equation Journal of Physics A. ,vol. 29, pp. 607- 633 ,(1996) , 10.1088/0305-4470/29/3/014
D. J. ARRIGO, J. M. HILL, P. BROADBRIDGE, Nonclassical symmetry reductions of the linear diffusion equation with a nonlinear source Ima Journal of Applied Mathematics. ,vol. 52, pp. 1- 24 ,(1994) , 10.1093/IMAMAT/52.1.1
M.C. Nucci, Iterating the nonclassical symmetries method Physica D: Nonlinear Phenomena. ,vol. 78, pp. 124- 134 ,(1994) , 10.1016/0167-2789(94)00125-1
Peter A. Clarkson, Martin D. Kruskal, New similarity reductions of the Boussinesq equation Journal of Mathematical Physics. ,vol. 30, pp. 2201- 2213 ,(1989) , 10.1063/1.528613