This paper is concerned with positive solutions of semilinear diffusion equations u
t=ε
2\ riangle u+u
p in Ω with small diffusion under the Neumann boundary condition, where p>1 is a constant and Ω is a bounded domain in R
N with C
2 boundary. For the ordinary differential equation u
t=u
p, the solution u
0 with positive initial data u
0∈ C(overline{Ω}) has a blow-up set S
0=\displaystyle {x∈overline{Ω}|u
0(x)=max_{y∈overline{Ω}}u
0(y)} and a blow-up profile \[u
*0(x)=(u
0(x)
-(p-1)-(max_{y∈overline{Ω}}u
0(y))
-(p-1))
-1/(p-1) \] outside the blow-up set S
0. For the diffusion equation u
t=ε
2\ riangle u+u
p in Ω under the boundary condition ∂ u/∂ v=0 on ∂Ω, it is shown that if a positive function u
0∈ C
2(overline{Ω}) satisfies ∂ u
0/∂ v=0 on ∂Ω, then the blow-up profile u
*ε(x) of the solution u
ε with initial data u
0 approaches u
*0(x) uniformly on compact sets of overline{Ω}\backslash S
0 as ε→+0.
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