The authors study the positive solutions of a semilinear parabolic system coupled by power nonlinearilities in a ball or in the whole space. A single-point blow-up result is proved for a large class of radial decreasing solutions, which answer the open problem posed by A. Friedman
and Y. Giga
[J. Fac. Sci., Univ. Tokyo, Sect. I A 34, 65–79 (1987; Zbl 0648.35042
)]. Finally, the author obtain the lower pointwise estimates for the final blow-up profiles.