Proper spaces for the asymptotic convergence of solutions of porous medium equation

In this paper, we consider the problem that a weighted L∞ space Wϑ(RN) is proper or not for the asymptotic convergence of solutions of the porous medium equation. We find that there exists a critical exponent ϑ=σ of the proper spaces for the asymptotic problem proposed by Alikakos and Rostamian (1984).