Institute of Mathematics of NAS of Ukraine,

3 Tereshchenkivs'ka Str.,

01601 Kyiv,

UKRAINE

E-mail: vaneeva@imath.kiev.ua, rop@imath.kiev.ua, ivanova@imath.kiev.ua

**Potential non-classical symmetries and exact solutions
of fast diffusion equation**

**Abstract:**

A fast diffusion equation is investigated with symmetry point of view.
The set of exact non-Lie solutions constructed by M.L. Gandarias [*Phys.
Lett. A*, 2001, **286**, 153-160] are supplemented with the similar
ones. The non-classical symmetries of the corresponding potential equation
are completely classified with respect to the Lie symmetry group of this
equation. As a result, we obtain new wide classes of potential non-classical
symmetries of the fast diffusion equation. It is shown that all known non-Lie
solutions of the fast diffusion equation are exhausted by ones which can
be constructed with the above potential non-classical symmetries.

For details see math-ph/0506067