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This paper is devoted to the study of a singular porous medium equation, which was studied extensively in recent years. We obtain the global existence and blow-up condition at the critical initial energy E(u0)=d$E(u_{0})=d$, while the previous papers only considered the case E(u0)<d$E(u_{0})< d$, where d is a positive constant which will be given in the main part of this paper.

Global existence and blow-up to the solutions of a singular porous medium equation with critical initial energy