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Source solutions for the nonlinear diffusion-convection equation

Published online by Cambridge University Press:  17 February 2009

G. C. Sander ,
R. D. Braddock ,
I. F. Cunning ,
J. Norbury  and
S.W. Weeks
G. C. Sander
Affiliation:
Faculty of Science and Technology Griffith University, Nathan 4111, Australia
R. D. Braddock
Affiliation:
Faculty of Environmental Sciences Griffith University, Nathan 4111, Australia
I. F. Cunning
Affiliation:
Faculty of Environmental Sciences Griffith University, Nathan 4111, Australia
J. Norbury
Affiliation:
Mathematical Institute, Oxford University24–29 St Giles, Oxford, OX1 3LB
S.W. Weeks
Affiliation:
Faculty of Science and Technology Griffith University, Nathan 4111, Australia
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Abstract

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In the paper King [8], a new class of source solutions was derived for the nonlinear diffusion equation for diffusivities of the form D(c) = D0cm/(l - vc)m+2. Here we extend this method for the nonlinear diffusion and convection equation

to obtain mass-conserving source solutions for a nonlinear conductivity function K(c) = K0cm+2/(l - vc)m+1. In particular we consider the cases m = -1,0, and 1, where fully analytical solutions are available. Furthermore we provide source solutions for the exponential forms of the diffusivity and conductivity as given by D(c) = D0c−2e−n/c and K(c) = K0ce−n/c.

Type
Research Article
Information
The ANZIAM Journal , Volume 39 , Issue 1 , July 1997 , pp. 28 - 45
Copyright
Copyright © Australian Mathematical Society 1997

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