| Abstract: |
| We consider a class of semilinear parabolic equations with singular potential on manifolds with conical singularities. At high initial energy level $J(u_0)>d$, we present a new sufficient condition to describe the global existence and nonexistence of solutions, respectively. Moreover, by applying the Levine`s concavity method, we give some affirmative answers to finite time blow up of solutions at arbitrary positive initial energy $J(u_0)>0$, including the upper bound of blowup time. Finally, we show a lower bound of the blowup time and blowup rate under arbitrary initial energy level. |
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