Invariant Sets and Exact Solutions to Nonlinear Diffusion Equations with x-Dependent Convection and Absorption |
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Authors: | JIA Hua-Bing XU Wei |
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Institution: | 1. Department of Applied Mathematics, Northwestern Polytechnical
University, Xi'an 710072, China
;2. Department of Mathematics, Baoji University of Arts and Sciences, Baoji 721013, China |
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Abstract: | In this paper, we introduce a new invariant set
?E0={u:ux=fˊ(x)F(u)+ε gˊ(x)
-fˊ(x)g(x)]F(u)exp(-∫u(1/F(z))dz), where f and g are some smooth functions of x, ε
is a constant, and F is a smooth function to be 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
?E0. |
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Keywords: | invariant set exact solution nonlinear diffusion equations rotation group scaling group |
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