SINGLE-POINT BLOW-UP FOR A SEMILINEAR REACTION-DIFFUSION SYSTEM

In this paper, we consider positive solutions of the system u(t)-Delta u = u(r)v(p) , v(t) - Delta v = u(q) v(s) t is an element of (0, T), x is an element of B(0, R) - {x is an element of R-n vertical bar vertical bar x vertical bar < R } or x is an element of R-n and p, q, r, s > 1. We prove single-point blow-up if r < q + 1 and s <: p + 1 and for a large class of radial decreasing solutions. This extends the result of Friedman and Giga for this basic system known only for p = q - r - s. We also obtain lower pointwise estimates for the blow-up profiles.