In this paper, we study a class of parabolic equations with critical Sobolev exponents and Hardy terms. Using Moser-type iteration, we characterize the asymptotic behavior of solutions at singular points. By means of critical point theory and the potential well method, we prove both global existence and finite-time blow-up depending on the initial datum.
"On a class of critical heat equations with an inverse square potential." Differential Integral Equations 20 (1) 27 - 50, 2007.