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

✍ Scribed by Christodoulos Sophocleous

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 234 KB
• Volume: 324
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/s0378-4371(03)00063-3

✦ Synopsis

We consider the variable coe cient inhomogeneous nonlinear di usion equations of the form f(x)ut =[g(x)u n ux] x . We present a complete classiÿcation 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) = x p and g(x) = x q we have the most known form of this class of equations. If certain conditions are satisÿed, then this latter equation can be transformed into a constant coe cient equation. It is also proved that the only equations from this class of partial di erential equations that admit Lie-B acklund symmetries is the well-known nonlinear equation ut = [u -2 ux] x and an equivalent equation. Finally, two examples of new exact solutions are given.