  We study the symmetry reduction of nonlinear partial differential equations
which are used for describing diffusion processes in nonhomogeneous medium. We
find ansatzes reducing partial differential equations to systems of ordinary
differential equations. The ansatzes are constructed by using operators of
Lie-B\"acklund symmetry of third order ordinary differential equation. The
method gives the possibility to find solutions which cannot be obtained by
virtue of classical Lie method. Such solutions have been constructed for
nonlinear diffusion equations which are invariant with respect to
one-parameter, two-parameter and three-parameter Lie groups of point
transformations.
