Behaviors of solutions for a singular diffusion equation

This paper is devoted to some behaviors of solutions of the initial-boundary problem for a singular diffusion equation, namely, localization and large time behavior. After given some special explicit solutions it is proved that solutions of the problem possess the localization property. Next, L2 decay estimate as t→∞ is proved by a rather standard energy method. Finally, by comparison with a special solution the expected L∞ decay estimate is derived.