Conditional Lie-Backlund symmetries and invariant subspaces to non-linear diffusion equations

In this paper, we consider the n-dimensional radially symmetric non-linear diffusion equations with source term u(t) = 1/r(n-1) [r(n-1)D(u)u(r)(m)](r) + Q(r, u). Equations admitting conditional Lie-B " acklund symmetries sigma = [g(u)](lr) + a(1)(r)[g(u)]((l-1)r) + ... + a(l)(r)g(u) are identified. The resulting equations associated with the invariant subspaces determined by the linear ordinary differential equation v(lr) + a(1)(r)(v(l-1)r) + ... + a(l)(r)(v) = 0 are either solved exactly or reduced to solving some finitedimensional dynamical systems.