Let u be a type I blowing up solution of the Cauchy-Dirichlet problem for a semilinear heat equation, ｛?_tu=?u+u~p, x∈?, t>0, u(x, t)=0, x ∈??, t>0, u(x, 0) = ф(x), x∈?, where ? is a (possibly unbounded) domain in R~N, N ≥ 1, and p > l. We prove that, if φ∈ L~∞(?) ∩ L~q (?) for some q ∈[1, ∞), then the blow-up set of the solution u is bounded. Furthermore, we give a sufficient condition for type I blowing up solutions not to blow up on the boundary of the domain ?. This enables us to prove that, if ? is an annulus, then the radially symmetric solutions of (P) do not blow up on the boundary ??.
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