A new blow-up condition for a parabolic equation with singular potential

This paper is aimed at giving a new blow-up condition of the following parabolic problem with singular potential|x|−sut−Δu=|u|p−2u, which was studied extensively in recent years. By constructing a new functional, we obtain some blow-up conditions which include the possibility of the initial energy J(u0)≥d, where d is a positive constant which will be given in the main part of this paper. The results of this paper extend previous results where only the case J(u0)