Consider the system
where , , and assume:
(1.5) , , if , ; , , if ,
(1.6) , if ; , if
Then there exists a unique classical solution of (1.1)-(1.4) in some , and , by the maximum principle. Let , for all as above. We claim
Further we assume that, for some ,
and that the solution (u,v) satisfies the estimates:
Then we see: Suppose that u and v solves (1.1), (1.2) with (1.3)-(1.6). If the conditions (2.1), (2.2) are satisfied, then there is a single blow-up point.