We consider singular solutions of a parabolic partial differential equation with power nonlinearity. It is known that in some range of parameters, this equation has a family of singular steady states with ordered structure. Our concern is the existence of time-dependent singular solutions and their asymptotic behavior, the convergence of solutions to singular steady states. Our method is based on the analysis of a related linear equation with a singular coefficient and the comparison principle. This is a joint work with Masaki Hoshino and Shota Sato.