Potential symmetries of inhomogeneous nonlinear diffusion equations
Date
2000Source
Bulletin of the Australian Mathematical SocietyVolume
61Issue
3Pages
507-521Google Scholar check
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In this paper potential symmetries are sought of the inhomogeneous nonlinear diffusion equations ut = x1-M [xN-1 f(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.