Abstract: This paper deals with the blow-up properties of solutions to the systems u_t △u=e^v(x₀,t), v_t-△v=e^v(x₀,t) in Ω×(0,T) subject to either initial conditions or the initial and boundary-value conditions. The authors show that under certain conditions the solution blows up in finite time and prove that the set of all blow-up points is the whole region. Moreover, the exact blow-up rates are also derived.

Key words: parabolic system, blow-up rate, blow-up set