抄録
We study the positive blowing-up solutions of the semilinear parabolic system: u
t-Δ u=v
p+u
r, v
t-Δ v=u
q+v
s, where t∈(0, T), x∈ \bm{R}
N and p, q, r, s>1. We prove that if r>q+1 or s>p+1 then one component of a blowing-up solution may stay bounded until the blow-up time, while if r<q+1 and s<p+1 this cannot happen. We also investigate the blow up rates of a class of positive radial solutions. We prove that in some range of the parameters p, q, r and s, solutions of the system have an uncoupled blow-up asymptotic behavior, while in another range they have a coupled blow-up behavior.
