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Three dimensional similarity solutions of the nonlinear diffusion equation from optimization and first integrals

Published online by Cambridge University Press:  17 February 2009

J.-Y. Parlange ,
R. D. Braddock ,
G. Sander  and
F. Stagnitti
J.-Y. Parlange
Affiliation:
School of Australian Environmental Studies, Griffith University, Nathan, Queensland 4111
R. D. Braddock
Affiliation:
School of Australian Environmental Studies, Griffith University, Nathan, Queensland 4111
G. Sander
Affiliation:
School of Australian Environmental Studies, Griffith University, Nathan, Queensland 4111
F. Stagnitti
Affiliation:
School of Australian Environmental Studies, Griffith University, Nathan, Queensland 4111
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Abstract

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For diffusion problems, the boundary conditions are specified at two distinct points, yielding a two end-point boundary value problem which normally requires iterative techniques. For spherical geometry, it is possible to specify the boundary conditions at the same points, approximately, by using an optimization principle for arbitrary diffusivity. When the diffusivity obeys a power or an exponential law, a first integral exists and iteration can be avoided. For those two exact cases, it is shown that the general optimization result is extremely accurate when diffusivity increases rapidly with concentration.

Type
Research Article
Information
The ANZIAM Journal , Volume 23 , Issue 3 , January 1982 , pp. 297 - 309
Copyright
Copyright © Australian Mathematical Society 1982

References

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