Open AccessExact solutions to the nonlinear diffusion-convection equation with variable coefficients and source term
Author(s) -
Hui Wan
Publication year - 2013
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.62.090203
Subject(s) - physics , exact solutions in general relativity , variable (mathematics) , diffusion equation , constant (computer programming) , term (time) , diffusion , convection , convection–diffusion equation , nonlinear system , mathematical analysis , fick's laws of diffusion , constant coefficients , mathematical physics , thermodynamics , mathematics , quantum mechanics , economy , economics , service (business) , computer science , programming language
The nonlinear diffusion-convection equation f(x)ut=(g(x)D(u)ux)x+h(x)P(u)ux+q(x)Q(u) with variable coefficients and source term has been studied. This equation is symmetrically reduced by the generalized conditional symmetry method. Some exact solutions to the resulting equations are constructed, with the diffusion terms D(u)=um (m≠-1,0,1) and D(u)=eu. These exact solutions are also the generalized functional separable solutions. Solutions to the equation with constant coefficients are covered by those exact solutions to the equation with variable coefficients.