ON THE BLOW-UP SET FOR U(T)=DELTA-U(M)-GREATER-THAN-1(U(M), M)

It is well known that every nan trivial solution of u(t) = Delta u(m) +u(m) in R-N x [0(,infinity)), u(x,0) = u(0)(x) greater than or equal to 0on R-N, with m > 1, blows up in finite time. We study the blow-up set and the blowup profile of a solution u(x,t) to this equation with blow-up time T > 0, under the assumption that u(0)(x) is compactly sup ported. We prove that, up to subsequences, (T-t)(1/(m-1))u(x,t) conver ges as t --> T to w(x). Here w(x) is a finite sum of translations with disjoint supports of the unique positive radially symmetric, compactl y supported, solution of Delta w(m) + w(m) - w/(m - I) = 0. The center s of these supports do not go beyond the smallest ball containing the support of u(0) and, u(x,t) remains uniformly bounded away from these supports. An estimate of the blow-up time is also provided.