ON CRITICAL EXPONENTS FOR A SEMILINEAR PARABOLIC-SYSTEM COUPLED IN ANEQUATION AND A BOUNDARY-CONDITION

In this paper, we consider the system [GRAPHICS] where R(+)(N)={(x(1), x')\x'is an element of R(N-1), x(1)>0},p,q>0, and u(0),v(0) are nonneg ative and bounded. We prove that if pq less than or equal to 1 every n onnegative solution is global. When pq>1 we let alpha=(p+2)/2(pq-1, be ta=(2q+1)/2(pq-1). We show that if max(alpha, beta)>N/2 or max(alpha, beta)=N/2 and p,q greater than or equal to 1, then all nontrivial nonn egative solutions are nonglobal; whereas if max(alpha,beta)<N/2 there exist both global and nonglobal nonnegative solutions. (C) 1996 Academ ic Press, Inc.