BLOW-UP ESTIMATES OF POSITIVE SOLUTIONS OF A REACTION-DIFFUSION SYSTEM

This paper is concerned with positive solutions of the reaction-diffusion system u(t) - Delta u = u(m1)v(n1) , v(t) - Delta v = u(m2)v(n2) which blow up at t = T. We obtain the following estimates on the blow-up rates: c(T- t)(-(n1-n2+1)/gamma) <= max(x is an element of Omega) u(x, t) <= C(T-t)(-(n1-n2+1)/gamma) c(T- t)(-(m2-m1+1)/gamma) <= max(x is an element of Omega) v(x, t) <= C(T-t)(-(m2-m1+1)/gamma) for some positive constants c,C and gamma = m(2)n(1), -(1 - m(1))(1 - n(2)).