  We investigate the relaxation to equilibrium of the solution of a class of
one-dimensional linear Fokker--Planck type equations that have been recently
considered in connection with the study of addiction phenomena in a system of
individuals. The steady states of these equations belong to the class of
generalized Gamma densities. As a by-product of the relaxation analysis, we
prove new weighted Poincar\'e and logarithmic Sobolev type inequalities for
this class of densities.
