Remarks on the blowup estimate for solution of the heat equation with a nonlinear boundary condition

This paper establishes the blowup estimate near the blowup time for the heat equation uₜ = Δ u with the nonlinear boundary condition uₙ = uᵖ on ∂ Ω× [0,T), where Ω is a bounded domain in RN. It is proved that the blowup will not occur in the interior of the domain. The blowup rate is established under certain conditio