Let Ω be a bounded smooth domain in RN. We consider the problem ut = u + V (x)up in Ω ×
[0,T ), with Dirichlet boundary conditions u = 0 on ∂Ω ×[0,T ) and initial datum u(x, 0) = Mϕ(x) where
M 0, ϕ is positive and compatible with the boundary condition.We give estimates for the blow-up time of
solutions for large values of M. As a consequence of these estimates we find that, for M large, the blow-up
set concentrates near the points where ϕp−1V attains its maximum.
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