Blow-up phenomena for a nonlocal semilinear parabolic equation with positive initial energy

This paper is concerned with the blow-up of solutions to the following semilinear parabolic equation: u t = Δ u + | u | p - 1 u - 1 | ¿ | ¿ ¿ | u | p - 1 u d x , x ¿ ¿ , t 0 , under homogeneous Neumann boundary condition in a bounded domain ¿ ¿ R n , n ¿ 1 , with smooth boundary.For all p 1 , we prove that the classical solutions to the above equation blow up in finite time when the initial energy is positive and initial data is suitably large. This result improves a recent result by Gao and Han (2011) which asserts the blow-up of classical solutions for n ¿ 3 provided that 1