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Potential symmetries of inhomogeneous nonlinear diffusion equations

Published online by Cambridge University Press:  17 April 2009

C. Sophocleous
C. Sophocleous
Affiliation:
Department of Mathematics and Statistics, University of Cyprus, CY 1678 Nicosia, Cyprus
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Abstract

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In this paper potential symmetries are sought of the inhomogeneous nonlinear diffusion equations ut = x1−M[xN−1f (u) ux]x. The functional forms of f (u) that admit such symmetries are completely classified. A complete list is presented of the symmetries, which depend on the values of the parameters M and N. We give examples of similarity solutions using potential symmetries. In some cases, the potential symmetries enable us to convert non–invertible mappings of nonlinear partial differential equations to linear ones.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 61 , Issue 3 , June 2000 , pp. 507 - 521
Copyright
Copyright © Australian Mathematical Society 2000

References

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