  The asymptotic behavior of a nonlinear diffusive equation obtained in the
framework of the $\kappa$-generalized statistical mechanics is studied. The
analysis based on the classical Lie symmetry shows that the $\kappa$-Gaussian
function is not a scale invariant solution of the generalized diffusive
equation. Notwithstanding, several numerical simulations, with different
initial conditions, show that the solutions asymptotically approach to the
$\kappa$-Gaussian function. Simple argument based on a time-dependent
transformation performed on the related $\kappa$-generalized Fokker-Planck
equation, supports this conclusion.
