Department of Applied Research,

Institute of Mathematics of NAS of Ukraine,

3 Tereshchenkivs'ka Str.,

01601 Kyiv-4, UKRAINE

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

**New results on group classification of nonlinear diffusion-convection
equations**

**Abstract:**

Using a new method and transformations Using a new method and transformations
of conditional equivalence, we carry out group classification in a class
of variable coefficient (1+1)-dimensional nonlinear diffusion-convection
equations of the general form f(x)u_{t} = (D(u)u_{x})_{x}+K(u)u_{x}.
We obtain new interesting cases of such equations with localized density
f, having large invariance algebra. Examples of Lie ansatze and exact solutions
of these equations are constructed.

The talk is based on our work math-ph/0306035.