On critical exponents for a semilinear parabolic system coupled in an equation and a boundary condition

[摘要] 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 nonnegative and bounded. We prove that if pq less than or equal to 1 every nonnegative solution is global. When pq>1 we let alpha=(p+2)/2(pq-1, beta=(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 nonnegative solutions are nonglobal; whereas if max(alpha,beta)

[发布日期] 1996-12-01