Symmetries and form-preserving transformations of generalised inhomogeneous nonlinear diffusion equations

Christodoulos Sophocleous

Physica A: Statistical Mechanics and its Applications, 2003, vol. 324, issue 3, 509-529

Abstract: We consider the variable coefficient inhomogeneous nonlinear diffusion equations of the form f(x)ut=[g(x)unux]x. We present a complete classification of Lie symmetries and form-preserving point transformations in the case where f(x)=1 which is equivalent to the original equation. We also introduce certain nonlocal transformations. When f(x)=xp and g(x)=xq we have the most known form of this class of equations. If certain conditions are satisfied, then this latter equation can be transformed into a constant coefficient equation. It is also proved that the only equations from this class of partial differential equations that admit Lie–Bäcklund symmetries is the well-known nonlinear equation ut=[u−2ux]x and an equivalent equation. Finally, two examples of new exact solutions are given.

Keywords: Nonlinear diffusion equations; Local and nonlocal symmetries; Form-preserving transformations (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:324:y:2003:i:3:p:509-529

DOI: 10.1016/S0378-4371(03)00063-3

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