The blow-up properties of solutions to a parabolic system with localized nonlinear reactions

摘要

This paper deals with the blow-up properties of solutions to the systems u_t - Δu = e~υ(x_o,t), υ_t - Δυ = e~u(x_o,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.